The Economics of Credence Goods: On the Role of Liability, Verifiability, Reputation and Competition

Transcription

1 DISCUSSION PAPER SERIES IZA DP No. 43 he Economics of Credence Goods: On the Role of Liability, Verifiability, Reutation and Cometition Uwe Dulleck Rudolf Kerschbamer Matthias Sutter February 29 Forschungsinstitut zur Zukunft der Arbeit Institute for the Study of Labor

2 he Economics of Credence Goods: On the Role of Liability, Verifiability, Reutation and Cometition Uwe Dulleck Queensland University of echnology Rudolf Kerschbamer University of Innsbruck and CEPR Matthias Sutter University of Innsbruck, University of Gothenburg and IZA Discussion Paer No. 43 February 29 IZA P.O. Box Bonn Germany Phone: Fax: Any oinions exressed here are those of the author(s) and not those of IZA. Research ublished in this series may include views on olicy, but the institute itself takes no institutional olicy ositions. he Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a lace of communication between science, olitics and business. IZA is an indeendent nonrofit organization suorted by Deutsche Post Foundation. he center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshos and conferences, data service, roject suort, research visits and doctoral rogram. IZA engages in (i) original and internationally cometitive research in all fields of labor economics, (ii) develoment of olicy concets, and (iii) dissemination of research results and concets to the interested ublic. IZA Discussion Paers often reresent reliminary work and are circulated to encourage discussion. Citation of such a aer should account for its rovisional character. A revised version may be available directly from the author.

3 IZA Discussion Paer No. 43 February 29 ABSRAC he Economics of Credence Goods: On the Role of Liability, Verifiability, Reutation and Cometition * Credence goods markets are characterized by asymmetric information between sellers and consumers that may give rise to inefficiencies, such as under- and overtreatment or market break-down. We study in a large exeriment with 936 articiants the determinants for efficiency in credence goods markets. While theory redicts that either liability or verifiability yields efficiency, we find that liability has a crucial, but verifiability only a minor effect. Allowing sellers to build u reutation has little influence, as redicted. Seller cometition drives down rices and yields maximal trade, but does not lead to higher efficiency as long as liability is violated. JEL Classification: C72, C9, D4, D82 Keywords: credence goods, exeriment, liability, verifiability, reutation, cometition Corresonding author: Matthias Sutter University of Innsbruck Deartment of Public Finance Universitaetsstrasse 5 A-62 Innsbruck Austria matthias.sutter@uibk.ac.at * We received helful comments from Dennis Dittrich, Winand Emons, Stehan Kroll, Wolfgang Luhan, and articiants at the Econometric Society Meeting in Wellington, the ENABLE-Meeting in Mannheim, the 3 rd Australian Worksho on Exerimental Economics in Melbourne, and seminar articiants at University of Bonn, IZA Bonn, University of Hannover, University of Stavanger, University of Vienna, Max Planck Institute of Economics Jena, and Queensland University of echnology. Financial suort from the Max Planck Society, the German Science Foundation (through the Gottfried Wilhelm Leibniz Price of the DFG, awarded to Axel Ockenfels) and the Austrian Science Foundation (FWF-grant P2796) is gratefully acknowledged.

4 I swear by Aollo the hysician and all the gods and goddesses that, according to my ability and judgment, I will kee this Oath and this stiulation: Into whatever houses I enter, I will go into them for the benefit of the sick and will abstain from every voluntary act of mischief and corrution... (Oath of Hiocrates, B.C.) Introduction Medical treatment is a rime examle of what is known as a credence good in the economics literature. Other examles include all tyes of reair services or the rovision of comlex goods like software rograms, but also seemingly straightforward goods like taxi rides in an unknown city can exhibit the roerties of credence goods. Generally seaking, credence goods have the characteristic that though consumers can observe the utility they derive from the good ex ost, they cannot judge whether the tye or quality of the good they have received is the ex ante needed one. Moreover, consumers may even ex ost be unable to observe which tye or quality they actually received. An exert seller, however, is able to identify the tye or quality that fits a consumer s needs by erforming a diagnosis. He can then rovide the right quality and charge for it, or he can exloit the information asymmetry by defrauding the consumer. An exert seller a car mechanic, for instance might have an incentive to cheat on a consumer in two dimensions: First, the reair might be inefficient. he mechanic might relace more arts than are actually necessary to bring the car back on the road (and charge for the additional time and material). his case is referred to as overtreatment because the additional benefits to the consumer are smaller than the additional costs. he mechanic s reair might also be insufficient, thus leaving the consumer with a bill, but with a car that is still not working roerly. his latter case is referred to as undertreatment since any material and time sent on the reair is ure waste. Second, the reair might be aroriate, but the mechanic might charge the consumer for more than he has actually done (e.g., by claiming to have changed a filter without having done so). his kind of roblem is known as overcharging and it can also lead to inefficiencies in the long run if the fear of getting

5 overcharged deters consumers from trading on credence goods markets in the future, thereby creating an Akerlof (97) tye of market breakdown. In this aer we resent an exeriment with 936 articiants. Desite the imortance of credence goods markets for many day-to-day decisions, this is the first large-scale exeriment on credence goods. It rovides controlled evidence of how institutional restrictions and market characteristics affect behavior on credence goods markets and how the inefficiencies arising from the asymmetric information on credence goods markets can be contained. Our exeriment is based on a full factorial design, varying the following factors: Liability, i.e. the necessity for the seller to rovide a good of sufficient quality to meet a consumer s needs. Verifiability of a seller s action, i.e. the necessity for the seller to charge for the good rovided. Reutation building, i.e. giving consumers the ossibility to identify their trading artners (as oosed to an anonymous market). Cometition, i.e. giving consumers an otion to choose from several sellers (as oosed to bilateral matching between sellers and consumers). We evaluate the exerimental behavior against two sets of redictions, one assuming standard (own-money-maximizing) references, and the other one considering non-standard references. Our formalization of non-standard references is motivated by the oening quote from Hiocrates, because the latter imlies a seller s concern for an aroriate treatment ( for the benefit of the sick ) and a renunciation of exloiting consumers ( abstain from every voluntary act of mischief and corrution ). For some exerimental treatment conditions, both models yield qualitatively very similar redictions. When the redictions differ, exerimental behavior seems to be better catured by the model with non-standard references, though. he exerimental results show that liability and cometition are the most imortant factors to increase trade on credence goods markets. If liability holds, the increase in trade causes an increase in efficiency. Without liability, the effect of increased trade on efficiency is ambiguous, because undertreatment occurs frequently. Verifiability of a seller s actions, although theoretically as owerful as liability, has only a minor imact. Similarly, the ossibility of reutation building is of negligible influence as long as liability or verifiability holds. Hence, our results suggest that legal liability clauses are most suitable to cure many of the inefficiencies associated with the rovision of credence goods. he remainder of the aer is organized as follows. In section 2 we discuss briefly related literature and how our exeriment can add insights and thus comlement the emirical 2

6 evidence. In Section 3 we describe the basic model and introduce the various conditions under which consumers and sellers might engage in trade. Section 4 contains the exerimental design. Section 5 derives hyotheses both for the cases of standard and non-standard references. Section 6 resents the exerimental results. Section 7 summarizes our main findings and discusses some olicy imlications. 2 Related Literature and Rationale for an Exerimental Study here are about two dozen theoretical contributions to the credence goods literature. he ioneering aer is by Darby and Karni (973), who introduced the term credence goods and added this tye of good to Nelson s (97) classification of ordinary, search and exerience goods. hey study how market conditions (the resence or absence of idle caacities, regulation, etc.) and reutation concerns affect the equilibrium amount of fraud (i.e., underand overtreatment, and overcharging). wo other imortant early contributions, both assuming verifiability and both studying a cometitive environment, are by Wolinsky. While Wolinsky (993) emhasizes that the informational asymmetry in credence goods markets might lead to secialization, Wolinsky (995) examines the role of customers search for multile oinions and exerts concerns for reutation in discilining exerts. aylor (995) rovides a theoretical micro-foundation of several imortant features observed in markets for credence goods (as, for instance, the heavy reliance on ex ost contracts and the revalence of free diagnostic checks), while Emons (997) studies the role of observability of caacities and treatments in inducing non-fraudulent behavior. Imortant recent theoretical contributions to the literature include Pesendorfer and Wolinsky (23), who exlore whether a cometitive samling of rices and oinions rovides incentives for exerts to rovide costly but unobservable diagnostic effort, and Alger and Salanie (26), who study a cometitive credence goods market in which exerts lie about the true diagnosis because an informed consumer would reject the rice offer to get the treatment from a cometing exert. A robust finding in this literature is that liability and verifiability are the most imortant institutional factors for exerts behavior, while reutation and cometition are imortant market factors (see Dulleck and Kerschbamer, 26, for details). Ordinary goods (such as etrol) have well-known characteristics, and subjects know where to get them. Search goods (like clothes) need to be insected before buying in order to observe their characteristics. Exerience goods (like wine) have unknown characteristics, but they are revealed after buying or consuming them. 3

7 he emirical evidence on the roblems with credence goods originates mainly from the market for car reairs and for health care services. Wolinsky (993, 995) refers to a survey conducted by the Deartment of ransortation estimating that more than half of car reairs are unnecessary, which is an indication of overtreatment. Hubbard (998) shows that car mechanics conduct vehicle insections differently deending on whether the vehicles are on warranty or not. Referring to the health care sector, the classic study by Fuchs (978) reorts a ositive correlation between the suly of doctors in a geograhical area and the cost and intensity of medical care. Emons (997) cites a Swiss study reorting that the average erson s robability of receiving one of seven major surgical interventions is one third above that of a hysician or a member of a hysician s family, indicating that a consumer s (resumed) education and information level affects the quality of treatment and the likelihood of overtreatment. He also mentions a study by the Federal rade Commission that documents the tendency of otometrists to rescribe unnecessary, but rofitable, treatment. Hughes and Yule (992) find that the number of cervical cytology treatments is ositively correlated with the fee for this treatment. Likewise, Gruber and Owings (996) and Gruber, Kim and Mayzlin (999) show that the relative frequency of Cesarean deliveries comared to normal child births reacts to the fee differentials of health insurance rograms for both tyes of treatments and to the intertemoral develoment of birth rates. Iizuka (27) investigates the Jaanese drug rescrition market where doctors often not only rescribe but also disense drugs. Controlling for atients health status, he finds that doctors rescritions resond to marku differences, i.e. to monetary incentives that are unrelated to warranted medication. 2 hough emirical studies on credence goods markets have documented the existence of inefficiencies, they generally lack a controlled variation of factors that might influence the level of efficiency. For instance, some aers show that overtreatment is haening, without systematically exloring the conditions leading to it (see, e.g., the case studies mentioned in Wolinsky 993 and 995, or Emons 997). Other studies vary only one articular asect that influences the rovision of credence goods for examle, the rice differential between Cesarean section deliveries and normal child births (Gruber et al., 999) without controlling for and varying other imortant factors (like liability or verifiability or reutation building of sellers). By running a controlled laboratory exeriment we are able to systematically vary 2 Afendulis and Kessler (27) show that the integration of diagnosis and treatment has raised the treatment costs of coronary artery disease. hey also find that under some conditions the integration of diagnosis and treatment can lead to better health outcomes, though. 4

8 several factors that may affect the rovision of credence goods, and identify the effects of these factors on sellers and consumers behavior. Field data are naturally limited in the number of conditions that can be varied. Hence, our exeriments comlement the emirical literature by allowing for a much broader variation of imortant factors under ceteris-aribus conditions. urning to the exerimental literature, closest to our aer are two articles by Huck, Lünser and yran (26, 27) who use a binary version of the well-known trust game (by Berg, Dickhaut and McCabe 995) and interret it as modeling a market for exerience goods. 3 Huck et al. (27) show that exerience goods are more efficiently rovided when sellers can build u reutation than if this is not the case. Yet, it does not make a difference whether buyers can only observe how a articular seller has served them in the ast or whether they know all ast quality choices of all sellers in the market. Introducing cometition (as comared to a bilateral matching of sellers and consumers), Huck et al. (26) find even higher efficiency levels than with reutation, because cometition lets sellers rovide high quality in the resent to attract consumers also in the future. aking a trust game as an examle for an exerience goods market limits the analysis of inefficiencies to undertreatment (low quality for a given rice) and no market interaction, though. he framework of credence goods is a much richer one as it adds oortunities for overtreatment and overcharging both of which constitute ersistent roblems on credence goods markets. It is noteworthy, however, that the setu of Huck et al. (26, 27) is a secial case of our more general model. In the final section of this aer we will exlain in more detail how the exerience goods model of Huck et al. (26, 27) is embedded in our model and how our results comare to theirs. 3 Exerience goods differ from credence goods in several imortant dimensions. For examle, () while the valuation of a consumer is strictly increasing in quality with exerience goods, it is constant whenever the quality is sufficient with credence goods; (2) for given rices a consumer can tell exactly which quality he refers in the case of exerience goods, but he does not know it with credence goods; (3) whereas the quality of the good is unobservable ex ante but erfectly observable ex ost with exerience goods, it may be observable either ex ante, or ex ost, or neither ex ante nor ex ost with credence goods. 5

9 3 A Simle Model of a Credence Goods Market 3. he Basic Model Consumers are ex ante identical and know that they need a major treatment (t h ) with robability h, and a minor treatment (t l ) with robability h. Each consumer (he) is randomly matched with one seller (she) who sets rices h and l for the major, resectively minor, treatment (with h l ). he seller has costs c h for the major treatment, and c l for the minor one (with c h > c l ). he consumer only knows the rices for the different treatments, but not the tye of treatment that he needs, when he makes his decision whether or not to interact with the seller. If the consumer decides against interaction then both the consumer and the seller receive an outside otion of o. In case of interaction, the seller gets to know which tye of treatment the consumer needs. hen she rovides one of the two treatments and charges one of the two rices. Consumers in need of the minor treatment t l are sufficiently treated in any case (receiving either t l or t h ). However, if the consumer needs the major treatment t h, then only t h is sufficient. A sufficient treatment yields a value v > for the consumer, an insufficient treatment yields a value of zero. 4 In case of an interaction, a consumer earns the value from being treated minus the rice to be aid, whereas a seller receives the rice charged minus the cost of the rovided treatment (c l if t l has been rovided, otherwise c h ). In the following, we extend this basic model in two stes. In extension we limit the action sace of the seller by considering liability and verifiability as institutional restrictions. In extension 2 we add reutation building and seller cometition as two imortant features of market interaction. 3.2 Extension : Liability and Verifiability Liability in credence goods markets imlies the requirement that sellers rovide a treatment that is sufficient to solve the consumer s roblem. hus, liability revents undertreatment, but it does not reclude overtreatment and/or overcharging. Verifiability 4 In order to kee the exosition as succinct as ossible, we resent the basic model as it will be imlemented in the exeriment. Of course, more general secifications would be ossible, such as varying the value of the outside otion with the tye of layer (seller vs. consumer) or the value from a sufficient treatment with the treatment needed by the consumer (minor vs. major treatment), or considering strictly ositive diagnosis costs (which we set zero here). Dulleck and Kerschbamer (26) discuss various generalizations, showing that many of them do not affect the theoretical results qualitatively. Hence, we use the simler framework, which also revents us from making the exeriment too comlicated for articiants. 6

10 means that consumers can observe and verify ex ost the treatment that has been rovided by the seller (without knowing, however, whether this treatment was needed). As a consequence, verifiability revents overcharging, but it does not reclude under- and/or overtreatment. he factorial combination of liability and verifiability creates four different institutional conditions that imly different sets of available actions for the seller (see Figure for the sequence of actions). ) In condition N (No Liability / No Verifiability) the seller is comletely free in her choice of treatment rovision and in which of the two osted rices she charges. 2) In condition L (Liability / No Verifiability) the seller must rovide a sufficient treatment. However, she is allowed to charge any of her osted rices. 3) In condition V (No Liability / Verifiability) the seller is not restricted in her choice of treatment, but she must charge the rice of the treatment actually rovided. 4) In condition LV (Liability / Verifiability) the seller must rovide sufficient treatment and charge the rice of the treatment actually rovided. Figure about here 3.3 Extension 2: Reutation and Cometition he basic model laces two articular restrictions on consumers. First, consumers cannot identify their (ast) trading artners. Second, consumers do not have a choice between different sellers, because they are bilaterally matched with one seller only. Our second extension lifts both restrictions, the first one by introducing an oortunity for reutationbuilding by making sellers identifiable, such that a consumer can kee track of his ast exerience with a articular seller (without knowing how this seller has treated other consumers, though). 5 he second restriction is removed by considering a cometition condition where consumers can choose among several sellers, knowing the rices osted by them. In this condition the matching becomes endogenous. We assume that consumers face zero costs when comaring the different sellers rices and sellers can treat more than one consumer (meaning that there are no caacity constraints). A factorial combination of allowing for reutation-building and seller cometition yields the following four market conditions. 5 Sellers can never identify consumers in our model, because we are rimarily interested in the effect of seller reutation. 7

11 ) In condition B (for baseline ; No Cometition / No Reutation) there is a bilateral matching of consumers and sellers, and consumers cannot identify their trading artners. 2) In condition R (No Cometition / Reutation) there is a bilateral matching of consumers and sellers, and a consumer knows whether a articular seller has treated him sufficiently or not in the ast and which rice she has charged. 3) In condition C (Cometition / No Reutation) consumers can choose among several sellers, but they cannot identify their trading artners. 4) In condition CR (Cometition / Reutation) consumers can choose among different sellers and they can identify them. able about here Combining both extensions yields 6 different conditions for the interaction between consumers and sellers on credence goods markets. able summarizes the different conditions and how they are characterized with resect to the resence or absence of liability, verifiability, reutation-building, and seller-cometition. 4 Exerimental Design 4. reatments, Parameters, and Matching he 6 conditions of interaction between consumers and sellers in able constitute the 6 different exerimental treatments of our study. Since we refer to sellers offering a treatment to consumers we will denote exerimental treatments as conditions throughout the aer. he abbreviations in able for the 6 conditions are of the form X/Y, where X {B, R, C, CR}, and Y {N, L, V, LV}. For examle, C/LV denotes the condition with seller cometition, where sellers can not build u reutation, but where both liability and verifiability aly. In the following we will often refer to a set of conditions by using a single element of the tules X/Y defined above. For instance, a reference to the set R includes all four conditions where reutation building is ossible, but where seller-cometition does not aly, i.e. set R includes R/N, R/L, R/V, and R/LV. In all exerimental conditions we let the consumer s robability of needing the major treatment be h =.5, and the value of a sufficient treatment be v =. he costs of roviding the minor (major) treatment is c l = 2 (c h = 6). he rices osted by the sellers, l and h (with 8

12 l h ), have to be chosen in integer numbers from the interval {, }. he outside otion if no trade takes lace is set to o =.6 both for the seller and the consumer. We always use matching grous of eight subjects each, which is common knowledge in all conditions. Four subjects in each matching grou are in the role of consumers, and four in the role of sellers. he assignment to roles is randomly determined at the beginning of the exeriment, and roles are ket fixed throughout the entire exeriment. here are 6 eriods of interaction between sellers and consumers in all conditions. Due to the reetition of the stage game, the matching of subjects is imortant. In the market conditions without reutation (i.e. in sets B and C) it must not be ossible for sellers to build u reutation in the course of the reeated interaction. his recludes the use of a artner matching (in which a seller would be matched with the same consumer in all 6 eriods). herefore, we use a stranger matching in which consumers and sellers are randomly rematched after each eriod. In the conditions with cometition (i.e. in sets C and CR) the four sellers have to ost rices first, and each of the four consumers is informed about the rices of all four sellers. Only then consumers have to choose with which seller, if any, to interact. Note that in condition C consumers cannot identify their (otential) trading artners. In order to make that more transarent, we stress in the exerimental instructions (see sulementary material) that the order of resenting the four sellers rices will be randomly determined in each eriod. Hence, seller x in eriod t need not be seller x in eriod t+. In the conditions with reutation-building (i.e., sets R and CR) consumers can kee track of their ast exerience with a articular seller through fixing the sellers IDs. he feedback consists of information on which seller they visited in a articular eriod, which rices had been osted in that eriod, and what was the consumer s rofit from the interaction. From the latter, consumers can infer whether they have been treated sufficiently or not and which rice has been charged. 4.2 Exerimental Procedure All exerimental sessions were run comuterized (using zree; Fischbacher, 27) and recruiting was done with ORSEE (Greiner, 24). A total of 936 undergraduate students articiated in the exeriment. All sessions started with an extensive descrition of the game. All arameters as well as the matching rocedure were made common knowledge to all articiants by reading them out aloud. Before the exeriment started, articiants had to answer a set of control questions correctly to ensure that they had fully understood the 9

13 instructions. For every session we invited four subjects more than needed in order make sure that we got enough subjects answering all questions correctly. Once the number of subjects required to start a session had answered all questions correctly, the four remaining subjects were aid 4 Euro and dismissed. he average session length, including instructions and control questions, was.5 hours. Particiants earned on average 4 Euro. 5 Predictions 5. Assuming Standard Preferences In this subsection we assume that both sellers and consumers are rational and only interested in their own monetary ayoff, and that this fact is common knowledge. We start by identifying equilibrium behavior for set B, after which we continue with sets R, C, and CR. Accomanying each rediction is a short rationale for it. he roofs are relegated to the sulementary material, Aendix A. able 2 summarizes the redictions, where row [] below each of the 6 conditions shows the redicted vector of rices osted by the seller and whether a consumer interacts with a seller or not. he first figure in curved arentheses refers to l, the second to h. For the conditions where interaction is redicted to take lace, row [2] indicates whether the consumer is aroriately treated ( efficient rovision ), undertreated, or overtreated, and row [3] refers to the seller s charging olicy. 6 able 2 about here 5.. Standard Predictions for Set B (Baseline) On the Role of Liability and Verifiability First note that under random matching and anonymity the redictions for the finitely reeated game are the same as the redictions for the underlying stage game. Since the stage game is solved through backward-induction we start (in rediction B S ) with the chronologically last decision in the stage game, which is the seller s rovision and charging olicy. hen we roceed backward through the game-tree (see Figure ) by addressing the 6 Here and throughout the article aroriate treatment refers to roviding t h if the consumer needs the major treatment and roviding t l if the consumer needs the minor treatment; undertreatment refers to roviding t l when the consumer needs t h ; overtreatment refers to roviding t h when the consumer needs t l.

14 consumer s accetance behavior (in rediction B S 2) and, finally, the seller s ricing olicy and the imlied rediction with resect to interaction (in rediction B S 3). In our characterization of those olicies we refer to the following tyes of rice-vectors: an equal mark-u rice-vector is defined as one that satisfies h l = c h c l = 4. an undertreatment rice-vector satisfies h l < c h c l = 4. an overtreatment rice-vector is characterized by h l > c h c l = 4. Prediction B S (Provision and Charging Policy). (i) In B/N sellers rovide the minor, but charge for the major treatment under each ricevector. (ii) In B/L sellers rovide the aroriate treatment and charge for the major treatment under each rice-vector. (iii) In B/V sellers rovide the aroriate treatment under equal mark-u vectors, but always the minor (major) treatment under undertreatment (overtreatment) rice-vectors. (iv) In B/LV sellers rovide the aroriate treatment under equal mark-u and undertreatment rice-vectors, but only the major treatment under overtreatment vectors. Prediction B S 2 (Accetance Behavior). Anticiating sellers behavior according to rediction B S, consumers accetance behavior deends exclusively on h, but not on l, when V is violated. When V holds, accetance behavior deends both on h and l. (i) In B/N consumers accet to be treated if and only if (iff) h 3. (ii) In B/L consumers accet to be treated iff h 8. (iii) In B/V consumers accet an equal mark-u vector iff h, they accet an undertreatment vector iff l 3, and an overtreatment vector iff h 8. (iv) In B/LV consumers accet an equal mark-u and an undertreatment vector iff ( l + h )/2 8, and they accet an overtreatment vector iff h 8. Prediction B S 3 (Pricing Policy and Interaction). Interaction always takes lace if either L or V (or both) holds; otherwise the market breaks down. With interaction, rices are such that sellers are induced to rovide the aroriate treatment and that the gains from trade accrue to the sellers. (i) In B/N the market breaks down. (ii) In B/L sellers ost a rice-vector with h = 8, l is indeterminate. (iii) In B/V sellers ost the equal mark-u vector {6, }.

15 (iv) In B/LV sellers ost an equal mark-u or an undertreatment vector with l + h = 6. Summarizing the standard redictions for set B we observe that if both liability and verifiability are violated, then the market breaks down. he reason is that in B/N sellers cannot be induced to rovide the major treatment and that always roviding the minor treatment generates exected gains from trade of only 3 (= ( - h)v c l ) which is less than the sum of two outside otions (2o = 3.2). hus, there exists no rice where both arties of the interaction get at least their outside otion. As soon as either L or V (or both) aly, however, sellers have an incentive to ost rices which induce them to rovide the aroriate treatment, making it rofitable for consumers to enter the market in all eriods in conditions B/L, B/V, and B/LV. his yields full efficiency then Standard Predictions for Sets R, C and CR On the Role of Reutation- Building and Cometition In discussing the influence of an oortunity for reutation-building and cometition on seller and consumer behavior we first resent the redictions when either reutation-building or cometition alies. Only after that we describe the effects if both aly jointly he Effects of Reutation Reutation-building itself does not change any of the redictions for set B since the stage game has a unique equilibrium and the reeated game a fixed, commonly known end date. Predictions R S to R S 3. Reutation itself does not affect the redicted behavior of sellers and consumers. Hence, redictions B S to B S 3 also aly to set R he Effects of Cometition he main effect of cometition is on the ricing olicy and the interaction frequency, while rovision and charging olicy are the same as in the baseline set B. Prediction C S (Provision and Charging Policy). Cometition itself does not affect the sellers rovision and charging olicy. Hence, rediction B S also alies to set C. In set B the matching between consumers and sellers is exogenous and the consumers only decision is to accet or reject the seller s offer. Hence, in set B the rediction on consumer behavior is a rediction on accetance behavior. With cometition, however, 2

16 consumers have to choose from a set of sellers, utting the determinants of this choice into the focus of analysis. o identify choice behavior, we will refer to rice-vectors e, u, o and eu. Among all equal mark-u vectors offered by the four sellers, e is the one with the lowest e = h - c h = l - c l. 7 Similarly, among all undertreatment (overtreatment) vectors, u ( o ) is the one with the lowest u = l - c l ( o = h - c h ). Finally, among all equal mark-u and all undertreatment vectors, eu is the one with the lowest eu = ( h - c h + l - c l )/2. 8 Prediction C S 2 (Visiting Behavior). When V is violated, a consumer s visiting behavior deends only on h, but not on l. When V holds, visiting behavior deends both on l and h. (i) In C/N consumers visit the seller (or one of the sellers) with the lowest h, rovided it satisfies h 3. Otherwise consumers abstain from interaction with sellers. (ii) In C/L consumers visit a seller with the lowest h, rovided it satisfies h 8. Otherwise consumers abstain from interaction. (iii) In C/V the following alies: - If e min{ u + 3, o + 2} consumers visit the seller (or one of the sellers) who osts e, rovided e 4. Otherwise consumers abstain from interaction. - If o min{ u +, e - 3} consumers visit the seller (or one of the sellers) who osts o, rovided o 2. Otherwise consumers abstain from interaction. - if u min { e - 4, o - 2} consumers visit the seller (or one of the sellers) who osts u, rovided u. Otherwise consumers abstain from interaction. (iv) In C/LV the following alies: - If eu o + 2 consumers visit the seller (or one of the sellers) who osts eu, rovided eu 4. Otherwise consumers abstain from interaction. - If eu > o + 2 consumers visit the seller (or one of the sellers) who osts o, rovided o 2. Otherwise consumers abstain from interaction. Prediction C S 3 (Pricing Policy and Interaction). Interaction (almost) always takes lace even in C/N, although sellers rovide only the minor treatment there. In conditions C/L, C/V 7 For convenience we denote not only a secific rice-vector but also the imlied mark-u by. 8 o be recise if { l i, h i } denote the rices osted by seller i then e =min i { h i -c h h i -c h = l i -c l }, u =min i { l i - c l h i -c h < l i -c l }, o =min i { h i -c h h i -c h > l i -c l }, and eu =min i {( h i -c h + l i -c l )/2 h i -c h l i -c l }. 3

17 and C/LV rices are chosen such that sellers are induced to rovide the aroriate treatment. In all conditions of set C the total gains from trade accrue to consumers. 9 (i) In C/N each seller osts {n.d, 3} with robability x =.844 and a rice-vector which is unattractive for consumers (due to h >3) with robability -x. If at least one seller osts {n.d, 3} then all consumers are (under-)treated, otherwise (with robability (-x) 4 =.6%) there is no interaction. Each seller s rofit in equilibrium is.6. (ii) In C/L each seller osts {n.d., 5} with robability x =.839 and {n.d., 6} with robability -x. Interaction always takes lace and consumers get aroriate treatment. Each seller s rofit in equilibrium is.64. (iii) In C/V each seller osts {3, 7} with robability x =.839 and {4, 8} with robability -x. Interaction always takes lace and consumers get aroriate treatment. Each seller s rofit in equilibrium is.64. (iv) In C/LV each seller osts either {4, 5} or {3, 6} with robability x =.32, either {5, 5}, or {4, 6}, or {3, 7} with robability y =.28, and either {5, 6} or {4, 7} with robability - x - y. Interaction always takes lace and consumers get aroriate treatment. Each seller s rofit in equilibrium is.683. he intuition for (almost) full interaction in C/N runs as follows. Although sellers can still not be induced to rovide the major treatment, each seller can now serve more than one consumer. he latter fact imlies that there is now room for rices that are rofitable for both arties of the interaction. Note, however, that the increase in the frequency of interaction 9 Here we focus on symmetric equilibria. Note that in the rice-osting stage of set C there are also asymmetric equilibria. Because there is no obvious way for sellers to coordinate on a secific asymmetric equilibrium we regard such equilibria as less lausible, and thus mention them only here in a footnote. Using similar techniques as in the roof of Prediction C S 3 it can be shown that the following are asymmetric equilibria (and in fact the unique equilibria in ure strategies): In C/N three sellers ost {n.d, 3} and one seller osts a ricevector which is unattractive for consumers (with h >3); the three sellers who ost {n.d, 3} earn.6493 in exectation, the forth seller gets.6 for sure. In C/L (C/V, resectively) three sellers ost {n.d., 5} ({3, 7}, resectively) and one seller osts a rice-vector that is less attractive for consumers; equilibrium rofits are as in C/N. In C/LV one seller osts {4, 5} or {3, 6} and three sellers ost rice-vectors that are less attractive for consumers; the seller osting the attractive rice-vector earns 2 for sure, the other three sellers get the outside otion. We round the robabilities of interaction to three decimals in this subsection. Note that within the three sets of rice-vectors, both sellers and consumers are indifferent which rice-vector is acceted. 4

18 translates only in a minor increase in efficiency (less than a /7 of the otential gains from trade are realized), as consumers are always undertreated in equilibrium he Combined Effects of Reutation and Cometition he main effect of combining cometition with reutation arises in the N-condition. In CR/N, cometition increases the frequency of interaction (in comarison to B/N and R/N) and reutation increases the efficiency of interaction (in comarison to C/N) by suorting equilibria with full interaction and aroriate treatment in early eriods. he reason is that consumers can now costlessly reward a seller who has treated them aroriately in the ast, simly by buying from this (and not from another) seller again even in the last eriods of the exeriment where sellers are known to act oortunistically in any case. Since L and/or V are already sufficient to yield full efficiency, we should find an effect of combining reutation and cometition on efficiency only in set N: Predictions CR S to CR S 3. Predictions C S to C S 3 remain equilibrium redictions also in set CR. In CR/N, there are additional equilibria where (some) sellers ost {n.d, 5} in the first 9 eriods and in which consumers accet, because they anticiate (correctly) that they will get the aroriate treatment with sufficiently high robability. Summarizing the standard redictions, we observe that either liability or verifiability or both lead to full efficiency while the absence of both leads to severe welfare losses. An oortunity for reutation building might substantially reduce the welfare losses, but only when combined with cometition. Cometition alone increases the frequency of interaction (without substantially increasing efficiency) if neither liability nor verifiability alies, but it has only redistribution effects (shifting the gains from trade from sellers to consumers) in all other cases. 5.2 Assuming Non-Standard Preferences So far we have assumed that subjects are rational and only interested in their own monetary ayoff. Motivated by the oening quote from Hiocrates, this section analyzes trade on credence goods markets when sellers have non-standard references. 2 More 2 o the best of our knowledge, Liu (28) is the only aer in the credence goods literature that considers sellers (or exerts) with non-standard references. She studies a credence goods market oulated by both 5

19 recisely, we assume that sellers care for aroriate treatment and correct charging. he former may be motivated by a desire for efficiency (see, e.g., Charness and Rabin, 22, for evidence on the behavioral relevance of efficiency-concerns) and the latter by a desire for honesty and keeing one s word (see Gneezy, 25, or Vanberg, 28, for evidence on how a concern for honesty or an aversion against cheating influences behavior). 3 We oerationalize a sellers desire for aroriate treatment and for honest charging as follows: Let θ {l, h} be the index of a consumer s tye of roblem, µ {l, h} the index of the treatment rovided and κ {l, h} the index of the treatment charged for. hen the utility of a seller of tye (α, β, γ) who is interacting with a consumer is assumed to be given by U α,β,γ ( l, h,θ,µ,κ) = κ c µ αi θ >µ βi θ<µ γi µ<κ, () where α is the disutility from undertreatment, β is the disutility from overtreatment, and γ is the disutility from overcharging a consumer. I is an indicator variable that takes the value of one if the condition in the subscrit is met and the value of zero otherwise. 4 he following redictions are based on the assumtion that sellers are heterogeneous. More recisely, we assume that sellers tyes are indeendently drawn from the same cumulative distribution G(α, β, γ) with strictly ositive density on [, α max ] x [, β max ] x [, γ max ]. 5 In the following we will sometimes refer to consumers having otimistic exectations. Consumers are said to have otimistic exectations if they believe that at least 52% of sellers have an α 4. A arameter of α 4 means that a seller s disutility from undertreatment is selfish and conscientious sellers. Selfish sellers simly maximize rofits while the utility of conscientious sellers is derived from rofits as well as from reairing the consumer s roblems. he key feature of Liu s (28) aer is that conscientious sellers are able to commit to treat consumers even if the rices they have osted do not cover treatment costs. hat is, in Liu s (28) model a conscientious seller has the same otions and ayoffs as a selfish seller excet that he cannot turn down a consumer after the diagnosis. Our formulation of non-standard references differs considerably from this aroach by keeing full freedom of action for the seller while allowing for a disutility from undertreatment, overtreatment or overcharging. 3 An aversion against undertreatment, overtreatment or overcharging is also imlied by Charness and Dufwenberg s (25, 26) they of guilt aversion (see also Battigalli and Dufwenberg, 27). In a nutshell, the theory of guilt aversion states that a layer i suffers from guilt to the extent that he believes that layer j i receives a lower ayoff than i believes j believes she will receive. A seller with guilt aversion may not rovide or charge for a wrong treatment if she does not want to disaoint the customer s beliefs about the ayoffs from the interaction. 4 Equation () uses the convention that l h, but not vice versa. 5 Note that the model introduced here collases to the case of standard references discussed in Section 5. if α max = β max = γ max =. 6

20 equal to or larger than the costs saved through undertreatment (i.e., αi θ >µ c h c l = 4). In some of the redictions we also refer to a variable x that is defined as x = ( h l ) (c h c l ) = h l 4. It is imortant to stress that we resent only those redictions based on non-standard (NS) references that differ from those derived in Subsection 5. under the assumtion of standard references. Note also that for more recise redictions it would have been necessary to assume a articular distribution of arameters α, β and γ across sellers and that this distribution is common knowledge. We abstain from such far-reaching, yet emirically not validated, assumtions Non-Standard Predictions for Set B (Baseline) On the Role of Liability and Verifiability Prediction B NS (Provision and Charging Policy). Contrary to the corresonding rediction with standard references, undertreatment, overtreatment and/or overcharging do not occur in all instances in which they are not revented by institutional safeguards (i.e., by liability or verifiability). Also, behavior changes continuously in the rice-difference h l instead of juming discontinuously as in the standard rediction. (i) Consider B/N and suose α max > 4 and γ max >. hen the undertreatment rate is below %. Furthermore, for rices satisfying h l < γ max the overcharging rate is below % and strictly increasing in the rice difference h l. (ii) Consider B/L and suose γ max >. hen for rices satisfying h l < γ max the overcharging rate is below % and strictly increasing in the rice difference h l. (iii) Consider B/V and suose α max > and β max >. hen for rices satisfying x (, α max ) the undertreatment rate is below % and strictly decreasing in the rice difference h l. Furthermore, for rices satisfying x (, β max ) the overtreatment rate is below % and strictly increasing in the rice difference h l. (iv) Consider B/LV and suose β max >. hen for rices satisfying x (, β max ) the overtreatment rate is below % and strictly increasing in the rice difference h l. 6 Strictly seaking, the non-standard redictions on the rovision and charging olicy are redictions for exogenously given rices. o check whether exogenously imosed rice vectors would yield different results we have run a control treatment where the rice vectors were redetermined by the exerimenter. he results of this robustness check are very briefly mentioned in footnote 2. Further details are available uon request. 7

21 Prediction B NS 2 (Accetance Behavior). Contrary to the corresonding rediction with standard references, the accetance behavior of consumers deends on l also in conditions B/N and B/L. Furthermore, accetance thresholds are higher. (i) Consider B/N, suose α max > 4 and that this is common knowledge. hen, for any { l, h } with l = h 8 there exist exectations such that a consumer with those exectations is willing to trade (in articular, a consumer might be willing to trade even if h > 3). Furthermore, for any { l, h } with l < h, h l < γ max and ( l + h )/2 8 there exist exectations such that a consumer with those exectations is willing to trade (in articular, a consumer might be willing to trade even if h > 8). (ii) Consider B/L, suose that γ max > and that this is common knowledge. hen for any { l, h } with l < h, h l < γ max and ( l + h )/2 8 there exist exectations such that a consumer with those exectations is willing to trade (in articular, a consumer might be willing to trade even if h > 8). (iii) Consider B/V, suose α max > and β max > and that this is common knowledge. hen for any { l, h } with x Min{α max, β max } and ( l + h )/2 8 there exist exectations such that a consumer with those exectations is willing to trade (in articular, a consumer might be willing to accet an undertreatment vector with l > 3, and an overtreatment vector with h > 8). (iv) Consider B/LV, suose β max > and that this is common knowledge. hen for any { l, h } with x< β max and ( l + h )/2 8 there exist exectations such that a consumer with those exectations is willing to trade (in articular, a consumer might be willing to accet an overtreatment vector with h > 8). Prediction B NS 3 (Interaction). Suose some consumers have otimistic exectations. hen there exists an equilibrium in which the frequency of interaction is strictly ositive even if neither observability nor liability (nor both) holds, that is, even in B/N, where rediction B S 3 redicts comlete market break down Non-Standard Predictions for Sets R, C and CR On the Role of Reutation- Building and Cometition he Effects of Reutation Allowing for heterogeneous sellers with resect to their references and for consumers with incomlete information about a seller s tye and her behavior creates reutation equilibria in the sirit of Kres and Wilson (982) and Milgrom and Roberts (982). In these equilibria it is attractive even for comletely selfish sellers (with α = β = γ = ) to incur short- 8

22 run costs to build u a reutation as a reliable seller in early eriods in order to be able to exloit the reutation in the final eriods of the finitely reeated game. In the following, we consider only R/N, since adding reutation when liability or verifiability already alies cannot imrove efficiency. Predictions R NS to R NS 3. Suose that α max > 4 and that this is common knowledge. Contrary to the rediction with standard references, equilibria exist in R/N in which the interaction frequency is % in early rounds and remains strictly ositive throughout the game and all sellers rovide the aroriate treatment in early rounds and some sellers rovide the aroriate treatment throughout the game he Effects of Cometition In the following rediction we refer to consumers with naïve exectations. Consumers are said to have naïve exectations if they assume that a seller s rovision olicy in C/N is indeendent of the rice-vector under which the consumer is treated. Note that naive exectations are fully justified in the benchmark of Subsection 5. (where α max = β max = γ max = ). Prediction C NS (Provision and Charging Policy). Suose that α max > 4 and that (some) consumers have naive exectations. hen undertreatment is higher in C/N than in B/N. Prediction C NS 2 (Visiting Behavior). Contrary to the corresonding rediction with standard references, consumers' visiting behavior deends on l also in conditions C/N and C/L. Summarizing the non-standard redictions, we observe that aroriate treatment might occur in equilibrium even without verifiability and liability and that aggregate behavior changes continuously in rice differences instead of being of the bang-bang variety as in the standard rediction. Also, in contrast to the standard rediction, an oortunity for reutation building might increase efficiency even in the absence of cometition. 9

23 6 Exerimental Results In line with the resentation of the basic model and its extensions in Section 3, subsection 6. deals with the imact of liability and verifiability in set B, and subsection 6.2 examines the effects of reutation and cometition. Subsection 6.3 illustrates the main effects of liability, verifiability, reutation and cometition on the basis of an econometric estimation. 6. Behavior in Set B (Baseline) Descritive analysis Main Result (On the Role of Liability and Verifiability): Liability has a highly significantly ositive imact on the frequency of interaction and on the degree of efficiency, as standard theory redicts. However, verifiability has no significant imact on those variables, contrary to the standard rediction. In fact, aggregate behavior is very similar between B/N and B/V, and the overall erformance in both conditions is better than the standard rediction for B/N, but worse than the standard rediction for B/V. Our model with non-standard references exlains only the better art of the latter result, but fails to account for the worse art. able 3 resents the main results for set B. he first row reveals that the average frequency of interaction between consumers and sellers is only around 5% in conditions without liability (B/N, B/V), but significantly higher and above 8% in conditions with liability (B/L, B/LV). 7 Looking at efficiency in the second row yields a similar icture. 8 Efficiency is below 2% without liability, but above 8% with liability. he third row reveals that, aart from the low frequencies of interaction, the high undertreatment rates (53% in B/N and 6% in B/V) are resonsible for the low efficiency in B/N and B/V. Overtreatment, by contrast, is no substantial roblem in any of the conditions (see fourth row). Hence, liability is crucial for behavior, while verifiability has no ositive effect in the aggregate, contrary to the standard theory s rediction. able 3 and Figure 2 about here 7 In able 3 we check for significant differences between two conditions each by using two-sided nonarametric Mann-Whitney U-tests (with a matching grou of 8 subjects constituting one indeendent observation). 8 Efficiency is defined as the ratio of the average actual rofit er subject to the average maximally ossible rofit er subject, where the outside otion is disregarded for both measures. 2

24 While able 3 resents overall averages, Figure 2 illustrates the develoment of key variables across the 6 eriods of the exeriment. Panel [A] shows that the frequency of interaction is rather stable, and high, if liability holds (in B/L and B/LV), while it has a steady downward trend whenever liability is violated (in B/N and B/V). Panels [B] to [D] dislay the time ath of undertreatment, overtreatment, and overcharging, showing in articular that overcharging is increasing over time, while there is no clear time trend for under- and overtreatment. Panels [E] and [F] show the develoment of (acceted) rices l and h, indicating that consumers are willing (and have) to ay the highest rices in conditions where liability alies. In the following, we resent for each of our redictions an accomanying result that adds further details. Result B (Provision and Charging Policy). (i) In B/N the undertreatment rate is 53%, which is far below the standard rediction of %. In fact, 3 out of 48 sellers always rovide the aroriate treatment across all 6 eriods. Whereas the standard rediction B S obviously fails to exlain this attern, rediction B NS with non-standard references can account for it. he non-standard rediction also imlies the attern observed with overcharging, as overcharging is below % and increasing in the rice difference h l. 9 (ii) In B/L the average overcharging rate is 65%, contrary to % according to rediction B S. In fact, twelve out of 48 sellers always charge for the actually rovided treatment even when h > l. Also, overcharging rate is increasing in the rice difference. 2 All those findings are consistent with rediction B NS, but not accounted for in the standard rediction B S. (iii) In B/V we observe equal mark-u vectors in only 4% of cases (29 out of 74), while in 94% of cases sellers ost an undertreatment rice-vector. For the former tye of ricevectors the standard model redicts aroriate treatment while we observe overtreatment in about 4% of the cases. For the latter tye of rice-vectors the standard model redicts 9 Overcharging occurs whenever the minor treatment is rovided, but the major treatment is charged, and h > l. For examle, holding the high rice constant at h = 8 (in B/N the high rice is at 8 in roughly 5% of rice-vectors), the relative frequency of overcharging is 75% when the low rice is l = 7, but increases monotonically to % with a decrease in the low rice down to l = 3. 2 For examle, holding the high rice constant at h = 8 (in B/L the high rice is at 8 in more than 8% of ricevectors), the relative frequency of overcharging is 65% when the low rice is l = 7, but increases monotonically to % with a decrease in the low rice down to l = 3. 2

25 undertreatment in all cases, while it is observed in only 6% of cases. While behavior under the former tye of rice vector is inconsistent with the non-standard model, behavior under the latter tye can be exlained by it. he non-standard rediction also catures the feature that the undertreatment rate is decreasing in the rice difference h l and that the overtreatment rate is increasing in it. 2 (iv) In B/LV equal mark-u vectors are extremely rare (2 out of 64 observations), the vast majority of rice-vectors (about 95%) are of the undertreatment tye. While the rovision behavior under undertreatment vectors is roughly consistent with both, the standard and the non-standard rediction, the rovision behavior under equal mark-u vectors (about 5% overtreatment) is not. Result B2 (Accetance Behavior). (i) In B/N consumers accet rice-vectors with average rices h = 7.28 and l = he standard-model would imly rejecting such high rices, yet for otimistic exectations accetance can be rationalized, as indicated in rediction B NS 2. he average rofits of consumers are only., however, which is less than their outside otion and shows that consumers exectations are too otimistic, on average. (ii) In B/L the average acceted h is 8., which is the oint rediction in B S 2, and which is also comatible with the non-standard rediction B NS 2. (iii) In B/V the overall average acceted l is 5.84, which seems fairly close to the standard model s redicted low rice of 6 in an equal mark-u rice-vector {6, }. Yet, as noted above, equal mark-u rice-vectors are extremely rare the vast majority (94%) of rice-vectors are undertreatment vectors. he standard rediction B S 2 imlies a lower rice of l = 3 under these circumstances, while the average l in acceted undertreatment vectors is For very otimistic exectations such accetance behavior is consistent with the nonstandard rediction B NS 2. However, consumers are again found to be too otimistic, since their average rofit is less than, and thus smaller than the outside otion. (iv) In B/LV the average acceted ( h + l )/2 under equal mark-u and undertreatment vectors is 7.46, which is roughly consistent with both sets of redictions. 2 For instance, the undertreatment rate is % for rice-vector {8, 8}, and it falls monotonically when the low rice is decreased ste by ste, reaching % for rice-vector {4, 8}. he overtreatment rate is % for vectors {7, 8} and {8, 8}, and it increases with a decrease in the low rice, reaching 38% for vector {4, 8}. In a control treatment (not reorted here) with exogenously given rices we found very similar results. 22

26 Result B3 (Pricing Policy and Interaction). (i) In B/N the most frequently osted rice-vectors are {6, 8} in 23% and {4, 8} in % of cases. he former would slit the gains from trade equally between sellers and consumers if sellers always rovided the aroriate treatment and always charged for the rovided treatment. he latter is an equal mark-u rice-vector. Comared to the standard rediction B S 3 osted rices are way too high (only 3 out of 768 cases had a high rice satisfying h 3). he non-standard rediction B NS 3 can account for interaction also taking lace with higher rices. (ii) In B/L sellers ost rice-vectors with h = 8 in more than 8% of the observations, which is largely consistent with the standard rediction. he most frequent rice-vectors are {6, 8} with 24%, and {7, 8} with 23% of cases. (iii) As noted above, in B/V sellers ost equal mark-u vectors in only 4% of cases, but undertreatment vectors in 94% of observations, which is in shar contrast to the standard rediction. he most oular rice-vectors are {6, 8} and {7, 8}, accounting for about 4%, resectively %, of observations. Such vectors are accetable if consumers exect sellers to have non-standard references (rediction B NS 2). (iv) In B/LV sellers almost always (in 96% of the observations) ost an undertreatment rice-vector, which is largely consistent with standard and non-standard references of sellers. he most rominent rice-vectors are {6, 8}, {7, 8} and {8, 8}, accounting for about 8% of the observations. As regards the relative frequency of interaction across the conditions in set B we note that the relatively high level in B/N (45% when the standard model redicts comlete market breakdown) can be exlained by some sellers having non-standard references and consumers having otimistic exectations (rediction B NS 3). However, the oor erformance of B/V can not be accounted for by any of our models, since they would not have redicted the almost universal use of undertreatment rice-vectors that yield strong incentives for undertreatment. Having liability of sellers increases the relative frequency of interaction significantly (to above 8%), though the level of interaction falls a bit short of the redicted %. 6.2 Behavior in Sets R, C and CR Descritive Analysis Main Result 2 (On the Role of Reutation-Building and Cometition): Set R. An oortunity for reutation building (without cometition) increases the frequency of interaction and decreases the frequency of overcharging when neither liability nor verifiability alies which is in line with the non-standard redictions R NS to R NS 3 while 23

27 inconsistent with the standard redictions R S to R S 3 but reutation building has no significant effect on behavior in all other cases which is consistent with both tyes of redictions. Set C. Cometition (without an oortunity for reutation-building) has a tremendous imact on the frequency of interaction, indeendently of whether liability and/or verifiability alies or is violated. For condition C/N, this effect of cometition is consistent with both the standard and non-standard redictions. In all other conditions both tyes of redictions did not suggest an effect on the frequency of interaction of adding cometition to the baseline set B, however. Set CR. Adding an oortunity for reutation-building to cometition has virtually no effect in comarison to behavior when only cometition alies, excet for condition N where adding R to C increases the frequency of interaction (without significantly affecting efficiency, however). able 4 resents the main results for all 6 exerimental conditions. Comaring across the four columns within each of the four anels [N], [L], [V], or [LV] allows checking how behavior is affected by cometition and reutation building, holding liability and verifiability constant. We use two-sided Mann-Whitney U-tests to indicate significant differences between two conditions each within a given anel. he overall attern emerging from able 4 is the following. (i) he frequency of interaction increases with cometition (with or without reutation). he imact of cometition on efficiency is ambiguous, however. In articular, efficiency is not increased by introducing C when liability and verifiability are both violated, but the imact is ositive in all other cases although the effect is only significant in V. Panel A of Figure 3 shows the develoment of the interaction frequency, confirming that it is always highest with cometition. (ii) here are no clear-cut effects of cometition on undertreatment, as can be seen from anel B of Figure 3. (iii) When verifiability alies both cometition and reutation increase overtreatment while there is no such effect when verifiability is violated, as can be seen in able 4 and in anel C of Figure 3. (iv) An oortunity for reutation building decreases overcharging in set N while there is no significant effect in all other conditions, as can be seen in able 4 and in anel D of Figure 3. 24

28 (v) Prices l and h are on average about 2 units lower with seller-cometition than without (see anels E and F of Figure 3). he gains from trade shift (almost comletely) from sellers to consumers when shifting from a condition without seller-cometition to one where sellers comete. able 4 and Figure 3 about here We add further details to the main result stated above by considering each of the redictions derived for behavior with reutation-building and/or cometition he Effects of Reutation in the Absence of Cometition Results R to R3. As exected from the non-standard (but not from the standard) rediction, we find that an oortunity for reutation building induces significant behavioral changes when neither liability nor verifiability alies whereas reutation has only a minor imact in all other cases: able 4 shows a significant increase in the frequency of interaction in R/N, comared to B/N. Likewise, overcharging decreases. Undertreatment was exected to decrease (see rediction R NS ), but this is not the case. An oortunity for reutation building seems to induce trust of consumers in sellers, hence the higher frequency of interaction, but trust does not ay in this condition, since the rofits of consumers are not higher in R/N than in B/N while those of sellers are significantly increased. In sum, adding an oortunity for reutation building has only imortant effects when there are no institutional safeguards against sellers misbehavior (in R/N), but reutation benefits the sellers only. his finding is roughly in line with the non-standard redictions R NS to R NS 3. Note, however, that the negative art of the redictions (no imact of reutation if either L or V or both aly) is based on the resumtion that the resence of L and/or V er se is already enough to yield full efficiency (so that adding R was exected to be of no hel). Since the actual frequency of interaction and degree of efficiency are rather low in set V, there would have been room for efficiency imrovements, which has not been exloited, though he Effects of Cometition in the Absence of Reutation Result C (Provision and Charging Policy). In conditions L, V and LV cometition alone does not have a significant influence on the rovision and charging olicy, as exected from the models with standard and non-standard references. In condition N, however, cometition 25

29 increases undertreatment from 53% to 73%, which is qualitatively in line with rediction C NS, even though it fails significance. able 5 about here Result C2 (Visiting Behavior). able 5 resents evidence on consumers visiting behavior. It shows the roerties of acceted rice-vectors. Standard theory redicts that consumers visit the seller with the lowest h if verifiability is violated, but that consumers visiting behavior deends on both rices if V holds. Looking at the uer anel of able 5 we see that, when V alies, the share of acceted rice-vectors that include the lowest rice h goes down, whereas rice-vectors with the minimum rice l (that do not also have the minimum rice h ) become more often acceted. 22 hus, consumers visiting behavior is largely in line with the standard theory s rediction C S 2. he strongest deviation can be found in C/N where in 32% of the observations a consumer does not visit the seller with the lowest h. Such behavior can be rationalized, though, when consumers exect sellers to have non-standard references (as assumed in rediction C NS 2). Result C3 (Pricing Policy and Interaction). (i) Whereas standard theory would have redicted a rice-vector with h = 3 (with any l u to h ) in C/N, rice-vectors with h 3 are chosen in less than % of cases. hus, average rices are too high to be consistent with standard redictions. he most rominent ricevectors are the equal mark-u vectors {3, 7} with 2% and {4, 8} with 8% of observations. he lower rices, comared to B/N, lead to a significantly higher interaction frequency (73% vs. 45%). (ii) According to the standard rediction rice-vectors of the tye {n.d., 5} should be osted in around 84% of observations in C/L, but they are roosed in only 3%. Vectors {n.d., 6} have been redicted in about 6% of cases, but observed in 33%. he most rominent vectors are again {3, 7} with 2% of observations, as well as {4, 8} and {5, 5} with 8% each. he frequency of interaction of 99% is at the edge of the redicted %. 22 Alying a χ²-test, we find that the distribution of acceted rice-vectors between rows a) and b) in able 5 is significantly different between C/N and C/V, and between C/L and C/LV ( <.5). Another way of stating this result is that the share of acceted rice-vectors that include the minimum rice h is significantly higher in C/N than in C/V, and also higher in C/L than in C/LV ( <.5). 26

30 (iii) In C/V sellers ost equal mark-u vectors in 23% of cases only, which is less than redicted by the standard model, but more than was observed in B/N. he redicted vector {3, 7} is the most rominent vector with %, and the alternative rediction of {4, 8} is observed in 8% of observations. he majority of vectors (64%) are undertreatment vectors. he most rominent ones of the latter tye are {5, 5} and {4, 6} with %, resectively 9%, of observations. he frequency of interaction is 88%, and thus is slightly below the redicted %. (iv) he set of rice-vectors exected from rediction C S 3 account for 5% of observations in C/LV. he most rominent vectors are {4, 6}, {4, 7}, and {3, 7} which account for % each. Undertreatment vectors are observed in 67% of cases, equal mark-u vectors in 23%. he relative frequency of interaction is 99%, and thus ractically identical to the redicted % he Combined Effects of Reutation and Cometition Results CR to CR3. Prediction CR S had indicated that adding reutation to cometition does not change any of the redictions, excet that it would admit equilibria in CR/N in which there is aroriate treatment in earlier eriods and, consequently, higher rices. We do not find evidence for this tye of equilibrium, though, since adding reutation-building kees both the undertreatment rate and the osted, resectively acceted, rices basically at the same levels as in C/N. Desite this, the relative frequency of interaction increases significantly (comare the entries for C/N and CR/N in able 4), again indicating that an oortunity of reutation building induces trust of consumers. When liability or verifiability (or both) alies, adding an oortunity for reutation building to cometition does not change any of the imortant variables substantially. his is a remarkable analogy to the revious results that adding reutation to the baseline condition has no effects as soon as either verifiability or liability alies. 27

31 6.3 Estimating the Effects of Liability, Verifiability, Reutation-Building and Cometition In able 6 we reort the coefficients from random effects robit regressions where we examine the imact of liability, verifiability, reutation-building and cometition on the relative frequency of interaction, undertreatment, overtreatment, and overcharging. 23 able 6 about here Column [] of able 6 considers the frequency of interaction on the seller side. 24 Looking at the main treatment effects one can see that liability and cometition have a significant effect, whereas verifiability and reutation er se are insignificant. All other things being equal, liability has a strong ositive effect on the likelihood of interaction, because consumers can be sure to receive a sufficient treatment. Cometition has a significant negative main effect on the robability of a articular seller having an interaction, since it leads to a concentration of several consumers visiting the same seller, leaving more sellers without any consumer. he row average # of consumers in able 4 shows that sellers have on average between.54 and 2.29 consumers er eriod in conditions with seller cometition. his concentration leaves other sellers without an interaction, hence the negative coefficient for cometition. Contrary to the standard (and non-standard) rediction, verifiability has no significant main effect. Reutation also lacks a significant main effect, consistent with the standard rediction. Both rices, l and h, have a significant negative effect on the likelihood of interaction. Recall that the standard rediction for conditions N and L (rediction B S 2) had 23 he models resented in able 6 were selected on the basis of the Bayesian Information Criterion for goodness of fit. Note that none of the third-order or fourth-order interaction effects of the main treatment variables liability, verifiability, reutation and cometition (as well as the interaction of these higher-order effects with eriod and rices) had been found significant when including them as indeendent variables. he model fit was also imroved by droing any interaction terms where either the eriod or any of the two rices ( l or h ) had been interacted with a second-order interaction of the main treatment variables (for examle, Period Liability Verifiability), since these terms were never significant. In columns [2] to [4] of able 6 we also dro the second-order interaction effects of the main treatment variables since BIC gets better (i.e., lower) by doing so. 24 We use the frequency of interaction on the seller (and not on the consumer) side as deendent variable here because among the indeendent variables there are the rices h and l and because in the cometition conditions (where consumers can choose from four rice-vectors) it would not be clear on which rices the frequency of interaction on the consumer side should be conditioned uon. 28

32 imlied that the low rice l has no imact on a consumer s accetance decision. his is obviously not what we observe. Rather, the low rice lures consumers into the market. Prediction B NS 2 accounts for this finding. Another noteworthy effect is the interaction of the high rice with verifiability. If verifiability holds, the negative main effect of the high rice h on the likelihood of interaction is reduced consistent with our non-standard rediction because an increase in the high rice renders undertreatment less attractive for sellers. Similarly, reutation has a ositive interaction effect with the high rice h, indicating that reutation building allows for a (relatively small) increase in the high rice without endangering the consumer s willingness to interact with the seller in set N. Finally note that the frequency of interaction is declining significantly across eriods, and that this downward trend is only artially offset when liability or verifiability alies. Figure 4 about here In anel [] of Figure 4 we show the estimated likelihood of interaction on the seller side for secific sets of indeendent variables, based on the estimation reorted in column [] of able 6. We consider only the final eriod of the exeriment (i.e., eriod 6), because we want to see how behavior looks like when subjects have exerience with the intricacies of credence goods markets. Furthermore, we fix the low rice at l = 4 on the left-hand side, resectively l = 5 on the right-hand side within each of the four sets N, L, V, and LV. For a given l we consider a high rice h {5, 6, 7, 8}. he attern emerging from the estimated likelihood of interaction illustrates the main results from able 6 very clearly. An increase in l or h decreases ceteris aribus the likelihood of interaction. Also, consistent with the nonstandard rediction, the negative imact of h on the likelihood of interaction is significantly lower in set V than in set N (since increasing h in conditions where verifiability holds decreases the undertreatment rate). Liability has a strong and ositive effect, whereas cometition has a negative one. Verifiability has a small effect. Reutation increases the likelihood of interaction if L is violated whereas it has no effect at all if L holds. his confirms our earlier finding that an oortunity for reutation building has only an imact if there is no institutional safeguard against sellers misbehavior. Remember that introducing an oortunity of reutation building increases the frequency of interaction in set N, but not in set V. he reason seems to be that the resence of R induces sellers to substantially increase h in set V, but that consumers are not willing to accet that increase (see h without interaction in anel [V] of able 4). 29

33 Column [2] of able 6 considers the likelihood of undertreatment. he most interesting finding from the viewoint of our redictions is the significant negative effect of the high rice h, whereas the low rice l is not significant. Note also that the interaction terms between both rices and V show the redicted sign and are highly significant. his imlies that the likelihood of undertreatment is decreasing in the rice difference h l, as exected from the non-standard redictions B NS, R NS, and C NS. Undertreatment also becomes more likely with more exerience across eriods. Desite its significantly ositive main effect, reutation does not increase the likelihood of undertreatment in total, because it has a negative interaction effect with rices. his can be much easier discerned from anel [2] of Figure 4, where it becomes clear that exerimental conditions with reutation have ceteris aribus the lowest likelihood of undertreatment. his is consistent with the non-standard rediction R NS. Comaring sets N and V reveals that an increase in the high rice h has a much stronger negative imact on the likelihood of undertreatment in set V than in set N, as the non-standard model redicts. As redicted, column [3] of able 6 reveals that the likelihood of overtreatment deends on the low and the high rice only in case verifiability alies. he negative interaction effect Price l Verifiability and the ositive interaction effect Price h Verifiability simly mean that overtreatment increases on average in the rice difference h l, as imlied by the non-standard rediction B NS. Panel [3] of Figure 4 shows that overtreatment is ractically non-existent as long as verifiability is violated (in sets N and L), while it increases with the high rice and decreases with the low rice in sets V and LV. Overcharging (see column [4] of able 6) deends only on a seller s rices. he likelihood of overcharging decreases with the low rice l and increases with the high rice h, as imlied by the non-standard redictions. his attern can also clearly be seen from anel [4] of Figure 4. From there we can also see that reutation decreases overcharging as indicated earlier. 3

34 7 Conclusion In this aer, we have analyzed behavior on credence goods markets. hese markets are rone both in reality and in our exeriment to roblems of undertreatment, overtreatment, and overcharging. We start the conclusion by noting that even under the most disadvantageous market conditions for consumers the sellers of credence goods have rovided an aroriate treatment in about half of the cases in our exeriment. Hence, even in the absence of liability laws, a large fraction of sellers is honest. his finding is much in the sirit of Hiocrates oath that we quoted in the beginning of this aer and which motivated our aroach for formulating redictions where sellers have non-standard references. his finding also means that social or moral norms (like not to exloit others or cheat on them) contribute to a considerable extent to the functioning of credence goods markets. In this aer we have been mainly interested in studying which other means besides an intrinsic motivation or moral commitment of sellers may yield efficient interaction on credence goods markets. More recisely, we have examined in a exerimental design the role of liability, verifiability, reutation, or cometition. Contrary to our redictions, verifiability has been found to have almost no effect (comared to a situation where only moral norms may aly). It seems safe to conclude, therefore, that forcing sellers of credence goods to charge only for the treatment they have rovided does not aroach the roots of the roblems. Hence, it cannot be an effective remedy of the roblems on credence goods markets to ask a car mechanic, for examle, to ut the relaced arts in the boot of the car in order to verify the resumed action. Liability to rovide a sufficient treatment has been found to have a very strong effect not only on the likelihood of trade on our exerimental credence goods markets, but also on its efficiency. It seems straightforward that liability makes it very attractive for consumers to trade with sellers, as undertreatment is recluded. However, liability does not solve the roblems of overtreatment (which may also create inefficiencies) or overcharging (which is another form of cheating on the consumer). It seems that consumers care most of all for the safety not to be treated insufficiently. Overtreatment or overcharging are of much less concern for consumers, and the likelihood of overtreatment or overcharging has not been affected by liability in our exeriment. Reutation-building has been found to be effective in increasing trade on credence goods markets, but only when none of the other effective means (liability and cometition, as it turns out) is resent. In this case (R/N), reutation-building benefits only the sellers, however, as they get more interaction (since consumers are more likely to trust them), but do not 3

35 change their behaviour (i.e., the undertreatment rate is not decreasing with reutation in the aggregate). Cometition among sellers has been found to be very influential in, first of all, bringing down the rices for credence goods (comared with a situation of a bilateral matching of sellers and consumers), and then increasing the frequency of trade on the market. his is not to say that cometition solves all the roblems on credence goods markets, because we have also found that the likelihood of undertreatment, overtreatment, or overcharging, is not reduced (but interestingly not increased either) through seller cometition. his means that the effects of cometition on trade are first and foremost driven by rice cuts through cometition, while the overall level of efficiency is not increased through cometition (excet when verifiability alies). As noted in the introduction, our aer is most closely related to two recent aers by Huck et al. (26, 27) where they study how reutation and cometition affect the efficiency on markets for exerience goods. Our model of a credence goods market can be seen as a generalization of their exerience goods market model. In articular, if we set the robability of needing the major treatment in our credence goods market equal to one (h = in our notation), then our N-conditions (B/N, R/N, and C/N) corresonded exactly to their design of a market for exerience goods. Huck et al. (27) comare the equivalents of our B/N- and R/N-condition, and Huck et al. (26) relate analogously B/N to C/N. Huck et al. (26, 27) reort retty large effects of reutation and cometition. Whereas cometition has also very strong effects in our design, we find much weaker effects of reutation. One ossible exlanation is that cheating is always detected in the set-u of Huck et al. (27) which makes a good reutation all the more valuable whereas in our design cheating may remain undetected. he latter ossibility weakens the imortance, and ultimately the effects, of reutation. It should also be noted that our design allows for a comarative assessment of reutation and cometition, and it also shows the comarative effects of liability and verifiability, both of which have been determined theoretically to be equally owerful to create efficiency in credence goods markets (Dulleck and Kerschbamer, 26). We conclude by noting that our analysis of the exerimental behavior has been guided not only by standard redictions (along the lines develoed in Dulleck and Kerschbamer, 26), but also by redictions that are based on non-standard references of sellers. In articular, we have studied a model where agents are motivated not only by own rofits but also by other motives such as those mentioned in the oath of Hiocrates. Excet for Liu (28) we are not aware of any model of credence goods markets that allows for non-standard 32

36 references. Our simle model with non-standard references has been found to exlain the behavior in credence goods markets in most cases better than a model with standard references. Scoe for further research is suggested by several unexlained observations, such as for instance the rominence of the rice-vector {6, 8} at the rice osting stage of the game and the frequent cases of overtreatment under equal mark-u rice-vectors. Both of these findings suggest that relative ayoffs matter for rovision behavior (the rice-vector {6, 8} slits the gains form trade equally between sellers and consumers if sellers always rovided the aroriate treatment and always charged for the rovided treatment; and most of the chosen equal mark-u vectors are such that aroriate treatment yields a higher monetary ayoff for the consumer than for the exert when the consumer has the minor roblem). One natural extension would therefore be to include relative ayoff concerns of agents in our model. he outcome-based models of Fehr and Schmidt (999) or Bolton and Ockenfels (2) may serve as a good starting oint in that resect. Another extension would be to consider concerns for recirocity in sequential and reeated interactions (in the sirit of Dufwenberg and Kirchsteiger, 24, for examle). While our simle model has abstracted from seller s exectations about the consumer s exectations, alying the theory of guilt aversion (Charness and Dufwenberg, 26; Battigalli and Dufwenberg, 27) to our model would add the imortant role of first-order and second-order exectations and their role for behavior on credence goods markets. hough all of these extensions romise to increase our knowledge of which conditions lead to more efficient trade on credence goods markets, they are beyond the scoe of this aer and are left for future research. 33

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38 Gneezy, U. (25), Decetion: he role of consequences. American Economic Review 95: Greiner, B. (24), An Online Recruitment System for Economic Exeriments. In: Kremer, K. and Macho, V. (eds.): Forschung und wissenschaftliches Rechnen 23. GWDG Bericht 63. Gesellschaft für Wissenschaftliche Datenverarbeitung, Göttingen, Gruber, J., Kim, J., Mayzlin, D. (999), Physician fees and rocedure intensity: he case of cesarean delivery. Journal of Health Economics 8: Gruber, J., Owings, M. (996), Physician financial incentives and Cesarean section delivery. RAND Journal of Economics 27: Hubbard,. N. (998), An emirical examination of moral hazard in the vehicle insection market. RAND Journal of Economics 29: Huck, S., Lünser, G., yran, J.-R. (26), Cometition fosters trust. UCL Working Paer. Huck, S., Lünser, G., yran, J.-R. (27), Pricing and trust. UCL Working Paer. Hughes, D., Yule, B. (992), he effect of er-item fees on the behavior of general ractitioners. Journal of Health Economics : Iizuka,. (27), Exerts agency roblems: Evidence from the rescrition drug market in Jaan. RAND Journal of Economics 38: Kres, D., Wilson, R. (982), Reutation and imerfect information. Journal of Economic heory 27: Liu,. (28), Credence goods markets with conscientious and selfish exerts. Working Paer. Milgrom, P., Roberts, J. (982), Predation, reutation and entry deterrence. Journal of Economic heory 27: Nelson, P. (97), Information and consumer behavior. Journal of Political Economy 78: Pesendorfer, W., Wolinsky, A. (23), Second oinions and rice cometition: Inefficiency in the market for exert advice. Review of Economic Studies 7: aylor, C. (995), he economics of breakdowns, checkus, and cures. Journal of Political Economy 3, Vanberg, C. (28), Why do eole kee their romises? An exerimental test of two exlanations. Econometrica 76: Wolinsky, A. (993), Cometition in a market for informed exerts services. RAND Journal of Economics 24: Wolinsky, A. (995), Cometition in markets for credence goods. Journal of Institutional and heoretical Economics 5:

39 ables and Figures able. he 6 Conditions of Interaction between Consumers and Sellers market condition B R C CR institutional condition N No Liability / No Verifiability L Liability / No Verifiability V No Liability / Verifiability LV Liability / Verifiability No Cometition / No Reutation No Cometition / Reutation Cometition / No Reutation Cometition / Reutation B/N R/N C/N CR/N B/L R/L C/L CR/L B/V R/V C/V CR/V B/LV R/LV C/LV CR/LV 36

40 able 2. Standard Predictions on Interaction and Pricing-, Provision- and Charging-Policy market condition institutional condition B No Cometition / No Reutation R No Cometition / Reutation C Cometition / No Reutation CR Cometition / Reutation N No Liability / No Verifiability [] [2] [3] B/N no interaction no rediction no rediction R/N no interaction no rediction no rediction C/N mixed eq.: high rob. on {n.d, 3} undertreatment overcharging CR/N mixed as in C/N; or {n.d.,5} in earlier rounds. undertr. or effic.. overcharging or honest charging L Liability / No Verifiability [] [2] [3] B/L {n.d., 8} efficient rovision overcharging R/L {n.d., 8} efficient rovision overcharging C/L mixed eq.: high rob. on {n.d, 5}, low rob. on {n.d., 6} efficient rovision overcharging CR/L mixed as in C/L; or {n.d., 5} efficient rovision overcharging or honest charging V No Liability / Verifiability [] [2] [3] B/V {6, } efficient rovision honest charging R/V {6, } efficient rovision honest charging C/V mixed eq.: high rob. on {3, 7}, low on{4, 8} efficient rovision honest charging CR/V mixed as in C/V; or {3, 7} efficient rovision honest charging LV Liability / Verifiability [] [2] [3] B/LV {6, },{7, 9}, or {8, 8} efficient rovision honest charging R/LV {6, },{7, 9}, or {8, 8} efficient rovision honest charging C/LV mixed eq.: high rob. on {5, 6} or {4, 7} efficient rovision honest charging CR/LV mixed as in C/LV; or {4, 5} or {3, 6} efficient rovision honest charging Legend [] rediction on interaction and (if alicable) on osted rices {x, y} seller osts rice x for t l and rice y for t h. n.d. not determined in theoretical solution mixed eq. equilibrium in mixed strategies rob. robability [2] rediction on rovision olicy undertr. undertreatment effic.. efficient rovision, i.e. roviding the treatment that is needed [3] rediction on charging olicy 37

41 able 3. Overview of Results in BASELINE (set B) B/N No Liability / No Verifiability B/L Liability / No Verifiability B/V No Liability / Verifiability B/LV Liability / Verifiability Averages er Period Interaction.45 a,c.82 a,d.5 d,f.82 c,f Efficiency 2.8 a,c.84 a,d.6 d,f.8 c,f Undertreatment, Overtreatment, Overcharging, 5.86 a.65 a - - l with Interaction 4.67 a,b,c 5.94 a,e 5.84 b,f 6.88 c,e,f l without Interaction 5.7 a,b,c 6.2 a,e 6.2 b,f 7.46 c,e,f h with Interaction 7.28 a,b,c 8. a,d 7.7 b,d,f 7.96 c,f h without Interaction 7.9 a,c 8.77 a,d 7.82 d,f 8.83 c,f Actually charged rice 7.8 a,b,c 7.77 a,d,e 6.44 b,d,f 7.46 c,e,f Profits Sellers a,c 3.44 a,d,e 2.58 d,f 3. c,e,f Profits Consumers 6. a,c 2.2 a,d,e.6 d,f 2.37 c,e,f Number of Subjects relative frequency 2 calculated as (actual average rofit outside otion) / (maximum ossible average rofit outside otion) 3 consumer needs t h, but seller rovides t l. 4 consumer needs t l, but seller rovides t h. 5 seller rovides t l, but charges t h (with h > l and consumer needing t l ) 6 in exerimental currency units Mann-Whitney U-tests for airwise differences between treatments (with matching grous of 8 subjects as one indeendent observation) a B/N vs. B/L ( <.5) b B/N vs. B/V ( <.5) c B/N vs. B/LV ( <.5) d B/L vs. B/V ( <.5) e B/L vs. B/LV ( <.5) f B/V vs. B/LV ( <.5) 38

42 able 4. Overview of Results Across All Conditions [N] No Liability / No Verifiability [L] Liability / No Verifiability Averages er Period B/N R/N C/N CR/N B/L R/L C/L CR/L Interaction on Cons. Side.45 a,b,c.63 a,d,e.73 b,d,f.85 c,e,f.82 b,c.76 d,e.99 b,d.98 c,e Avg. # of Consumers Interaction on Seller S a,c.63 a,d.47 d,f.55 c,f.82 b,c.76 d,e.43 b,d.43 c,e Efficiency d,e.92 d.96 e Undertreatment Overtreatment c c Overcharging 7.86 a,b,c.53 a.65 b.5 c l with Interaction 4.67 b,c 5.9 d,e 3.9 b,d 3.3 c,e 5.94 b,c 5.47 d,e 3.36 b,d 3.6 c,e l without Interaction 5.7 b 5.72 d 4.6 b,d b 6.7 d 4.3 b,d 4.23 h with Interaction 7.28 b,c 7.6 d,e 5.73 b,d 6.33 c,e 8. b,d 8.2 d,e 5.72 b,d 5.76 c,e h without Interaction b 9. d 7.64 b,d 7.55 Actually aid rice 7.8 b,c 7.4 d,e 5.35 b,d 5.8 c,e 7.77 b,c 7.56 d,e 5.42 b,d 5.24 c,e Profits Sellers a 3.2 a,d 2.36 d b,c 2.98 d,e.23 b,d.9 c,e Profits Consumers b,d 2.24 d,e 4.56 b,d 4.7 c,e Number of Subjects [V] Verifiability / No Liability [LV] Liability / Verifiability Averages er eriod B/V R/V C/V CR/V B/LV R/LV C/LV CR/LV Interaction on Cons. Side.5 b,c.6 d,e.88 b,d.93 c,e.82 b,c.76 d,e.98 b,d.99 c,e Avg. # of Consumers Interaction on Seller S b,c.76 d,e.43 b,d.52 c,e Efficiency 4.6 b,c.3.34 b.46 c.8.7 d,e.88 d.93 e Undertreatment 5.6 c c Overtreatment 6.5 a,b,c.2 a.3 b.9 c.3 b,c.7.2 b.9 c Overcharging l with Interaction 5.84 b,c 5.74 d,e 4.6 b,d 3.99 c,e 6.88 b,c 6.48 d,e 4.9 b,d 4.2 c,e l without Interaction 6.2 b 6.3 d 4.84 b,d b,c 6.75 d,e 4.59 b,d 4.43 c,e h with Interaction 7.7 b,c 7.69 d 6.4 b,d 6.97 c 7.96 b,c 8.4 d,e 6.9 b,d 6.38 c,e h without Interaction 7.82 a 8.38 a b,c 9. d,e 7.94 b,d 7.65 c,e Actually aid rice 6.44 b,c 6.6 d,e 5.9 b,d 5.58 c,e 7.46 b,c 7.39 d,e 5.44 b,d 5.49 c,e Profits Sellers b,c 2.5 e.96 b.9 c,e 3. b,c 2.83 d,e.5 b,d.3 c,e Profits Consumers 8.6 b,c.53 e 2.8 b 2.59 c,e 2.37 b,c 2.37 d,e 4.5 b,d 4.49 c,e Number of Subjects relative frequency of consumers interacting with a seller 2 average number of consumers treated by a seller who has at least one consumer 3 relative frequency of sellers interacting with at least one consumer 4 calculated as (actual average rofit outside otion) / (maximum ossible average rofit outside otion) 5 relative frequency of consumer needs t h, but seller rovides t l. 6 relative frequency of consumer needs t l, but seller rovides t h. 7 relative frequency of seller rovides t l, but charges t h (with h > l and consumer needs t l ) 8 in exerimental currency units a B vs. R ( <.5) b B vs. C ( <.5) c B vs. CR ( <.5) d R vs. C ( <.5) e R vs. CR ( <.5) f C vs. CR ( <.5) 39

43 able 5. Visiting Behavior when Cometition Alies (sets C and CR) C (Cometition / No Reutation) C/N C/L C/V C/LV Relative frequency with which an acceted rice-vector included a) the minimum rice h (irresective of order of l ) b) the minimum rice l (but not the minimum rice h ) c) neither of the above # observations CR (Cometition / Reutation) Relative frequency with which an acceted rice-vector included CR/N CR/L CR/V CR/LV a) the minimum rice h (irresective of order of l ) b) the minimum rice l (but not the minimum rice h ) c) neither of the above # observations

44 able 6. Panel Probit Regressions Using Data from All Conditions [] Interaction on seller side [2] Undertreatment [3] Overtreatment [4] Overcharging indeendent variables Liability (L = ) 5.45 ** n.a Verifiability (V = ) n.a. Reutation (R = ) ** Cometition (C = ) -.85 * Price l -.3 ** ** Price h -.46 ** -.22 **.2.55 ** Price l Liability.3 n.a Price h Liability -.56 ** n.a..3.3 Price l Verifiability ** -.52 ** n.a. Price h Verifiability. ** -.8 **.33 ** n.a. Price l Reutation -.6 * -.8 * Price h Reutation.8 * -.8 *.8.4 Price l Cometition Price h Cometition * -.2 Period -.8 **.7 ** -.7 **.2 Period Liability.4 ** n.a Period Verifiability.3 ** -.5 **.5 ** n.a. Period Reutation Period Cometition Intercet 4.75 **.4 * -.52 **.49 Liability Verifiability -. Liability Reutation -.4 ** Liability Cometition -2.6 ** Verifiability Reutation -. Verifiability Cometition.26 * Reutation Cometition -.4 # Observations 7,488,225 2,92,366 Bayesian Information Criterion (BIC) 8,44.73,58.6,45.96,495.3 ** (*) significant at the % (5%) level. n.a. not alicable, i.e. a given action (deendent variable) is not ossible in a articular condition (indeendent variable) he two-way interaction terms of main treatment variables (L, V, R, C) have not been included in the regressions for undertreatment, overtreatment and overcharging due to model selection based on BIC. 4

45 Figure. he Four Institutional Conditions N (No liability / No Verifiability) out outside otion t h h, l in h -h tl t h seller osts rices customer enters or not nature determines severity of roblem h l h l h l h l t l seller treats seller charges L (Liability / No Verifiability) out outside otion h, l in h -h t h t h t l seller osts rices customer enters or not h l h l h l nature determines severity of roblem seller treats seller charges V (No Liability / Verifiability) out outside otion h t h h, l in h -h tl l h t h seller osts rices customer enters or not nature determines severity of roblem t l seller treats l seller charges LV (Liability / Verifiability) out outside otion h, l in h -h t h t h t l seller osts rices customer enters or not h h l nature determines severity of roblem seller treats seller charges 42

46 Figure 2. Interaction, Provision-, Charging- and Pricing-Policy in Set B [A] Relative frequency of interaction [B] Average rate of undertreatment B/N B/L B/V B/LV B/N B/V Period Period [C] Average rate of overtreatment B/N B/L B/V B/LV Period B/N [D] Average rate of overcharging B/L Period [E] Average acceted rice l [F] Average acceted rice h B/N B/L B/V B/LV 4 B/N B/L B/V B/LV Period Period 43

47 Figure 3. Develoment of Behavior Across All Conditions A. Relative frequency of interaction on consumer side Set N (No Liability / No Verifiability) Set L (Liability / No Verifiability) B R C CR B R C CR Period Period Set V (No Liability / Verifiability) Set LV (Liability / Verifiability) B R C CR Period B R C CR Period B. Relative frequency of undertreatment Set N (No Liability / No Verifiability) Set V (No Liability / Verifiability) B R C CR Period.2. B R C CR Period 44

48 Figure 3 - continued C. Relative frequency of overtreatment Set N (No Liability / No Verifiability) B R C CR Set L (Liability / No Verifiability) B R C CR Period Period Set V (No Liability / Verifiability) B R C CR Period Set LV (Liability / Verifiability) B R C CR Period D. Relative frequency of overcharging Set N (No Liability / No Verifiability) B R C CR Period Set L (Liability / No Verifiability) B R C CR Period 45

49 Figure 3 - continued E. Acceted rice l Set N (No Liability / No Verifiability) Set L (Liability / No Verifiability) B R C CR 2 B R C CR Period Period Set V (No Liability / Verifiability) Set LV (Liability / Verifiability) B R C CR 2 B R C CR Period Period F. Acceted rice h Set N (No Liability / No Verifiability) Set L (Liability / No Verifiability) B R C CR 4 B R C CR Period Period Set V (No Liability / Verifiability) Set LV (Liability / Verifiability) B R C CR 5 4 B R C CR Period Period 46

50 Figure 4. Predicted Likelihood of Behavior in Period 6 [] Likelihood of interaction on seller side Set N (No Liability / No Verifiability) B R C CR l = 5 l = 4 h = 5 h = 6 h = 7 h = 8 h = 5 h = 6 h = 7 h = Set L (Liability / No Verifiability) B R C CR l = 4 l = 5 h = 5 h = 6 h = 7 h = 8 h = 5 h = 6 h = 7 h = Set V (No Liability / Verifiability) l = 4 l = 5 B R C CR h = 5 h = 6 h = 7 h = 8 h = 5 h = 6 h = 7 h = Set LV (Liability / Verifiability) l = 5 l = 4 B R C CR h = 5 h = 6 h = 7 h = 8 h = 5 h = 6 h = 7 h = 8 [2] Likelihood of undertreatment Set N (No Liability / No Verifiability) l = 4 l = 5 B R C CR h = 5 h = 6 h = 7 h = 8 h = 5 h = 6 h = 7 h = Set V (No Liability / Verifiability) l = 4 l = 5 B R C CR h = 5 h = 6 h = 7 h = 8 h = 5 h = 6 h = 7 h = 8 25 Likelihood of seller having one (or more) consumers for interaction 47

51 Figure 4 continued [3] Likelihood of overtreatment Set N (No Liability / No Verifiability) B R C CR l = 4 l = 5 h = 5 h = 6 h = 7 h = 8 h = 5 h = 6 h = 7 h = Set L (Liability / No Verifiability) B R C CR l = 4 l = 5 h = 5 h = 6 h = 7 h = 8 h = 5 h = 6 h = 7 h = Set V (No Liability / Verifiability) B R C CR l = 4 l = 5 h = 5 h = 6 h = 7 h = 8 h = 5 h = 6 h = 7 h = Set LV (Liability / Verifiability) B R C CR l = 4 l = 5 h = 5 h = 6 h = 7 h = 8 h = 5 h = 6 h = 7 h = 8 [4] Likelihood of overcharging Set N (No Liability / No Verifiability) l = 5 l = 4 B R C CR h = 5 h = 6 h = 7 h = 8 h = 6 h = 7 h = Set L (Liability / No Verifiability) B R C CR h = 5 h = 6 h = 7 h = 8 h = 6 h = 7 h = 8 48

52 Sulementary material accomanying he economics of credence goods On the role of liability, verifiability, reutation and cometition Not intended for rint ublication Aendix A. Derivation of Predictions hroughout we assume that a consumer who is indifferent between visiting an exert and not visiting an exert decides for a visit, and that a customer who is indifferent between two or more exerts randomizes (with equal robability) among them. he equilibrium concet we aly is Perfect Bayesian Equilibrium (PBE). Our main focus is on symmetric equilibria. In many cases there are also asymmetric equilibria. However, given that there is no obvious way for sellers to coordinate on a secific asymmetric equilibrium we regard such equilibria as less lausible and mention them only in footnotes. As in the main text, sellers are female, consumers are male. Standard Predictions Predictions B S to B S 3 as well as redictions C S and C S 2 follow from Dulleck and Kerschbamer (26), and redictions R S to R S 3 follow from the arguments in the text. Here we rove the rest of the redictions. Prediction C S 3 (Pricing Policy and Interaction). he following are symmetric mixed strategy equilibria of the rice osting stage of the game: (i) In C/N each seller osts {n.d, 3} with robability x = and a rice-vector which is unattractive for consumers (due to h >3) with robability -x. If at least one seller osts {n.d, 3} then all consumers are (under-)treated, otherwise (with robability (-x) 4 =.6%) there is no interaction. Each seller s rofit in equilibrium is.6. (ii) In C/L each seller osts {n.d., 5} with robability x = and {n.d., 6} with robability -x. Interaction always takes lace and consumers get aroriate treatment. Each seller s rofit in equilibrium is.638. We round the robabilities to five decimals in this subsection.

53 (iii) In C/V each seller osts {3, 7} with robability x = and {4, 8} with robability -x. Interaction always takes lace and consumers get aroriate treatment. Each seller s rofit in equilibrium is.638. (iv) In C/LV each seller osts either {4, 5} or {3, 6} with robability x =.3227, either {5, 5}, or {4, 6}, or {3, 7} with robability y =.283, and either {5, 6} or {4, 7} with robability - x - y. Interaction always takes lace and consumers get aroriate treatment. Each seller s rofit in equilibrium is Proof: Suose a (=, 2, 3, 4) sellers ost rice-vectors among which consumers are indifferent while the other 4 a sellers ost rice-vectors that are less attractive for consumers. hen the robability that one of the a sellers gets exactly b (=,, 2, 3, 4) customers is given by 4b 4 a Pba ( ) = b a a Consider condition C/N and therein seller i. Suose the other three sellers behave as secified in the rediction. hen, from i's ersective, the robability that exactly c (=,, 2, 3) of the other three sellers ost {n.d, 3} is given by 3 3 c W(c ) = ( x) c ( x) c In equilibrium, seller i is indifferent between offering a rice-vector that is unattractive for consumers (which gives him a ayoff of.6 for sure) and osting {n.d, 3} which generates an exected ayoff of Wc ( ) Pbc ( + )* b+ P( c+ )* (A) c= b= hus, setting (A) equal to.6 and solving for x gives the x-art of the result, the rest is obvious. he argument for conditions C/L and C/V is similar, the only difference being that in those conditions the less attractive rice-vector (with a mark-u of 2) also otentially attracts customers 2 thereby increasing the exected ayoff of a seller who osts the unattractive rice-vector from.6 (the value of the outside otion) to ( - W())*.6 + W()* (Σ 4 b= P(b 4)*2b)+ P( 4)*.6 >.6. (A2). b 2 he high rice offer {n.d., 6} ({4, 8}, resectively) attracts customers if no seller osts {n.d., 5} ({3, 7}, resectively). 2

54 hus, in conditions C/L and C/V setting (A) equal to (A2) and solving for x gives the x-art of the result and inserting x into (A) (or into (A2)) gives equilibrium rofits. Condition C/LV is slightly more comlicated. In that condition three different classes of rice-vectors are otential candidates for equilibrium rice-vectors, vectors in class (consisting of {4, 5} and {3, 6}) yield an exected rofit of.5 er customer, vectors in class 2 (comrising {5, 5}, {4, 6} and {3, 7}) yield er customer and vectors in class 3 (i.e., {5, 6} and {4, 7}) yield.5 er customer. 3 Using similar techniques as before it is (burdensome but) straightforward to show that there is no symmetric equilibrium in which sellers lace strictly ositive robability only on vectors in a single class or on vectors in two different classes and that there is a unique symmetric mixed strategy equilibrium in which sellers randomize among vectors in all three classes. All vectors in the suort of the mixed strategy must attract the same exected rofit; this determines x, y and equilibrium rofits. Predictions CR S to CR S 3. Predictions C S to C S 3 remain equilibrium redictions also in set CR. In CR/N, there are additional equilibria where (some) sellers ost {n.d, 5} in the first 9 eriods and in which consumers accet, because they anticiate (correctly) that they will get the aroriate treatment with sufficiently high robability. Proof: Consider the following strategies and beliefs: Consumers Beliefs: Each consumer believes that each seller always charges h indeendently of the rice-vector under which he is treated. He believes to be served efficiently iff (a) he is treated under a {n.d, 5} rice-vector and the seller has at least two customers; (b) the seller has either never undertreated him before or has only undertreated him in a situation where all sellers had exactly one customer; and (c) the game is in any of the rounds If at least one of (a)-(c) is not fulfilled, the consumer believes to always get the minor treatment. Consumers Strategy: In round consumers randomize with equal robability among sellers who have osted {n.d, 5}. If no seller has osted {n.d, 5}, they randomize with equal robability among sellers who have osted {n.d, 3}. If there is neither a seller who has osted {n.d, 5} nor a seller who has osted {n.d, 3} then they refrain from interacting. In rounds 2 to 9, among the sellers who are exected to serve efficiently, the consumer chooses the one with 3 Notice that vectors in a given class are exchangeable from both the consumers and the sellers ersective because the ex ante exected rice and the ex ante exected rofit is the same for all vectors in a class. 4 When a consumer decides which seller (if any) to visit, he does not know whether a seller will serve two or more customers, of course. 3

55 strictly the most customers in the revious round; if no seller had strictly the most customers in the revious round (i.e. in the case where each seller had exactly one customer or where two sellers had two customers each) consumers randomize with equal robability among sellers who are exected to serve efficiently. If no seller is exected to serve efficiently, the consumer randomizes with equal robability among sellers who have osted {n.d, 3}. If there is neither a seller who is exected to serve efficiently nor a seller who has osted {n.d, 3} then the consumer refrains from interacting. In rounds -6 consumers buy from sellers offering {n.d, 3}. If there is more than one such seller they choose the one that served most customers in round 9 unless they were undertreated in any of rounds -9 by this seller in a situation where the seller had more than one customer. In the latter case they randomize among the remaining sellers offering {n.d, 3}. If there is no seller who offers {n.d, 3} they refrain from interacting. Sellers Strategy: In rounds -9: All sellers ost {n.d., 5}; they serve customers efficiently if they have two or more customers and rovide low quality otherwise. In rounds -6: If one seller had strictly the most customers in round 9, all sellers ost {n.d., 3} and always deliver low quality; otherwise, i.e. if each seller had exactly one customer or two sellers had two customers each, then all sellers lay the mixed equilibrium as outlined in Prediction C S 3 (i). We now verify that these strategies and beliefs form a PBE. First notice that consumers beliefs reflect sellers strategy. Next consider consumers strategy. In rounds -9 consumers strategy is rational, because the minimum exected ayoff from interacting in these rounds at rices {n.d., 5} is larger than the outside otion: he only case where a consumer may be undertreated is if he ends u as a single customer with a seller. his is only ossible if the game is in round or no seller had strictly the most customers in the revious round. In this case each consumer has an incentive to articiate because the ayoff from using a random seller in the current round is [.5 +.5*( )]*5 -.5*.75 3 *5 = >.6 where the term in square brackets is the robability that a consumer is efficiently treated - i.e. he needs t l, or he needs t h and at least one other consumer visits the same seller. 5 In rounds -6 a consumer s behavior is rational either because he is undertreated under {n.d, 3} (yielding an exected ayoff of 2) or because he is not served at all (yielding the outside otion). Finally consider sellers strategies: We start with the behavior in rounds -6. wo events are to be 5 If in a revious round one seller had strictly the most customers, all customers are treated efficiently for sure, ie. the ayoff is 5. 4

56 considered: a) One Seller had strictly the most customers in round 9. In that case that seller has all the customers from round onwards rovided she did not deliver t l to a customer who needed t h in round 9. Given that future customer behavior is not affected, always delivering low quality is a dominant strategy for this seller. he other three sellers have no ossibility of getting more than the outside otion, thus their behavior is otimal too. b) No seller had a strict majority of customers in round 9. In this case the reasoning of the roof of rediction C S 3 (i) alies. Next consider round 9. hree cases are to be considered. a) One seller has 3 or 4 customers in this round, i.e. a certain strict majority of consumers. In that case serving all customers efficiently guarantees a maximum additional future ayoff of 6.8 (= 7*2.4) in rounds -6 which is strictly more than the maximum additional current ayoff from deviating (which is equal to 6 in the case that the seller serves four consumers who all need t h ). 6 b) A seller has exactly two customers in this round. Given the behavior of consumers, the conditional robability that she is the seller with a strict majority of customers given that she has exactly two customers is equal to (3*/3*2/3) / [3*(/3) 2 + (3*/3*2/3)] = 2/3. hus, the exected additional future ayoff from treating efficiently is 6.8*2/3 =.2 which is strictly more than 8, the maximum additional current ayoff from deviating (if both consumers need t h ). 7 c) If a seller has only one customer in round 9 there is no additional future ayoff from treating efficiently and she will therefore cheat. he arguments for rounds -8 are similar to those for round 9, the main difference being that the additional exected future ayoff from treating efficiently is higher, the incentives to deviate therefore lower. Non-Standard Predictions Prediction B NS (Provision and Charging Policy). (i) Consider B/N and suose α max > 4 and γ max >. hen the undertreatment rate is below %. Furthermore, for rices satisfying h l < γ max the overcharging rate is below % and strictly increasing in the rice difference h l. (ii) Consider B/L and suose γ max >. hen for rices satisfying h l < γ max the overcharging rate is below % and strictly increasing in the rice difference h l. 6 Mistreating only one of the customers yields an additional current rofit of 4 and a loss in future rofit of 7, mistreating tow of the customers yields an additional current rofit of 8 and a loss in future rofit of 4, etc. 7 Here notice that there is no additional exected future ayoff from treating efficiently if exactly two sellers have two customers each in round 9. 5

57 (iii) Consider B/V and suose α max > and β max >. hen for rices satisfying x (, α max ) the undertreatment rate is below % and strictly decreasing in the rice difference h l. Furthermore, for rices satisfying x (, β max ) the overtreatment rate is below % and strictly increasing in the rice difference h l. (iv) Consider B/LV and suose β max >. hen for rices satisfying x (, β max ) the overtreatment rate is below % and strictly increasing in the rice difference h l. Proof: Part (i): Since c h - c l = 4, sellers with an α > 4 will abstain from undertreatment. hus, if α max > 4 the undertreatment rate must be below % given our assumtion of a strictly ositive density on the suort [, α max ] x [, β max ] x [, γ max ]. Sellers with γ > will only overcharge if h - l > γ. hus, for (exogenously given) rices satisfying h - l < γ max the overcharging rate is below % and increasing in h - l due to our full suort assumtion. he argument for arts (ii), (iii) and (iv) is similar. Prediction B NS 2 (Accetance Behavior). (i) Consider B/N, suose α max > 4 and that this is common knowledge. hen, for any { l, h } with l = h 8 there exist exectations such that a consumer with those exectations is willing to trade (in articular, a consumer might be willing to trade even if h > 3). Furthermore, for any { l, h } with l < h, h l < γ max and ( l + h )/2 8 there exist exectations such that a consumer with those exectations is willing to trade (in articular, a consumer might be willing to trade even if h > 8). (ii) Consider B/L, suose that γ max > and that this is common knowledge. hen for any { l, h } with l < h, h l < γ max and ( l + h )/2 8 there exist exectations such that a consumer with those exectations is willing to trade (in articular, a consumer might be willing to trade even if h > 8). (iii) Consider B/V, suose α max > and β max > and that this is common knowledge. hen for any { l, h } with x Min{α max, β max } and ( l + h )/2 8 there exist exectations such that a consumer with those exectations is willing to trade (in articular, a consumer might be willing to accet an undertreatment vector with l > 3, and an overtreatment vector with h > 8). (iv) Consider B/LV, suose β max > and that this is common knowledge. hen for any { l, h } with x< β max and ( l + h )/2 8 there exist exectations such that a consumer with those exectations is willing to trade (in articular, a consumer might be willing to accet an overtreatment vector with h > 8). 6

58 Proof: Part (i): Consider a rice-vector { l, h } with l = h = and suose a consumer exects that x% of the sellers who offer such a vector have an α 4 (since α max > 4 such exectations are feasible for any x ). hen he is willing to accet iff x [( +.6)/5 - ]. Setting x equal to and solving for yields 8.4. Similarly, if γ max > then rices that fulfil ( l + h )/2 8.4 and h - l < γ max are attractive to customers who lace sufficient weight on α realizations in [4, α max ] and γ realizations in [ h - l, γ max ]. he roof for arts (ii) to (iv) is similar. Prediction B NS 3 (Interaction). Suose some consumers have otimistic exectations. hen there exists an equilibrium in which the interaction frequency is strictly ositive even if neither observability nor liability (nor both) holds (that is, even in B/N, where rediction B S 3 redicts comlete market break down). Proof: First notice that sellers with α 4 are committed to deliver t h to consumers of tye t h. Knowing this, they will never offer a rice-vector { l, h } with h < 6. herefore a ooling PBE involving constant rices must have l = h 6. Suose (i) that all sellers offer { l, h } = {6, 6}, (ii) that oortunistic exerts (sellers with α < 4) always rovide the minor treatment under each rice-vector while committed exerts (sellers with α 4) always rovide the aroriate treatment under each rice-vector, and (iii) that consumers exectations are correct along the equilibrium ath. hen consumers with otimistic exectations (execting that at least 52% of sellers offering {6, 6} have a α 4) are willing to accet since [ /2] 6.6 = o. he term in the squared brackets is the robability to be served sufficiently meeting a committed exert (α 4) with robability 52%, and meeting a non-committed seller (α<4) with robability 48%, but needing only t l (with robability ½). Predictions R NS to R NS 3. Suose that α max > 4 and that this is common knowledge. Contrary to the rediction with standard references, equilibria exist in R/N in which the interaction frequency is % in early rounds and remains strictly ositive throughout the game and all sellers rovide the aroriate treatment in early rounds and some sellers rovide the aroriate treatment throughout the game. Proof: We are searching for a Kres-Wilson-Milgrom-Roberts tye of good reutation equilibrium in which oortunistic exerts (sellers with α < 4) mimic committed exerts 7

59 (sellers with α > 4) in early rounds. For commitment tyes only rice-vectors with h 6 are rofitable, we therefore search for a PBE in which all tyes ool on { l, h } = {6, 6}. In equilibrium consumers exect (i) that exerts osting { l, h } = {6, 6} will serve them efficiently in early rounds (the meaning of in early rounds will be secified below) while exerts osting other rice-vectors will undertreat them throughout the game, and (ii) that only committed exerts osting { l, h } = {6, 6} will serve them efficiently in later rounds while oortunistic exerts will undertreat them later on. Consumers revise their exectations if and only if they are undertreated in early rounds. In this case they infer that the resective exert is an oortunistic one who will undertreat them in any future interaction. Consumers interact with a seller osting { l, h } = {6, 6} iff they have not been undertreated in an earlier round by this seller and they interact with a seller osting a different rice-vector iff this rice-vector has h 3. Committed exerts (sellers with α 4) offering { l, h } = {6, 6} always rovide the aroriate treatment while oortunistic exerts (sellers with α < 4) offering { l, h } = {6, 6} rovide the aroriate treatment until round and always the minor treatment in eriods +, +2,...,6. 8 We search for that eriod until which there exists no incentive for an oortunistic seller to undertreat because this would lead to a loss of business in the future 9. Let v x = [(4 - x)*4 + x*.6] / 4 denote the (exected) value of a round in which x (=,, 2, 3, 4) customers reject treatment because they have been undertreated by this seller before. Also, let x =(4+x)/8 denote the robability that at the end of a round the number of customers willing to interact with a seller is the same as at the beginning of the round given that (i) x customers are willing to interact with the seller at the beginning of the round and (ii) the seller rovides the minor treatment in the current round. Finally, let V denote the exected value of all future interactions, including the current one, given that (i) the seller has rovided aroriate treatment to all customers u to eriod, (ii) the seller rovides the minor treatment to a customer with the major roblem in eriod, and (iii) the seller rovides the minor treatment in all eriods succeeding. hen V 6 = v and for < 6 8 Given this trigger strategy of consumers it is straightforward to see that if a seller undertreats in eriod t she will also undertreat in eriod t + as the (otential) loss in business decreases in the number of rounds layed. 9 he incentive not to undertreat comes from the fact that the customer may return in the future with a minor roblem which then generates a rofit that can comensate for the forgone oortunity to undertreat. his robability is the sum of the robability that a customer wishes not to interact because he was undertreated before - x/4 - lus the robability that the customer interacts but only needs low quality and hence cannot be undertreated - (4-x)/4*.5. 8

60 9 = = = = = = = t t s s t r r s t t s r t t s s t t s t t t v I v I v I v I V V ) )( )( ( ) )( ( ) ( 5 Next, let W denote the exected value of all future interactions including the current one given that (i) the seller has rovided aroriate treatment to all customers u to eriod, (ii) the seller rovides the major treatment to a customer with the major roblem in eriod, and (iii) the seller rovides the minor treatment to her customer in all eriods beyond. hen W 6 = and for < 6 = = = = = = = = = = = t t s s t r r s t q q r s t t s r q t t s s t r r s t t s r t t s s t t s t t t v I v I v I v I v I W W ) )( )( )( ( ) )( )( ( ) )( ( ) ( 5 We are searching for the highest integer for which W > V. Solving this roblem (with Mathematica) yields = 2. hus, in the first two rounds it is rofitable for oortunistic sellers to mimic committed ones, while in later rounds it is not. Prediction C NS (Provision and Charging Policy). Consider set N, suose that α max > 4 and that (some) consumers have naive exectations. hen undertreatment is higher in C/N than in B/N. Proof: From rediction B NS 3 we know that if some consumers have otimistic exectations then there exists a ooling PBE in which the interaction frequency is strictly ositive even if neither observability nor liability (nor both) holds (that is, even in B/N). In this equilibrium (i) all sellers ost { l, h } = {6, 6}, (ii) oortunistic exerts (sellers with α < 4) always rovide the minor treatment and (iii) committed exerts (sellers with α 4) always rovide the aroriate treatment. hus, if at least one committed seller oulates the market, then the he Mathematica notebook yielding this result is available from the authors uon request.

61 undertreatment rate in this market is below % in B/N. Now consider C/N. If consumers have not only oortunistic but also naive exectations then they believe that exerts behavior does not deend on the rices they ost. hus, oortunistic exerts can undercut their committed rivals because a h < 6 yields a lower ayoff to commitment tyes than no interaction at all. hus, if at least one oortunistic exert oulates a market, committed exerts are driven out of business in that market leading to an undertreatment rate of % in that market (and to a higher undertreatment rate on average over all markets in C/N).

62 Aendix B. Exerimental Instructions (for condition CR/LV instructions for the other conditions are available uon request) INSRUCIONS FOR HE EXPERIMEN hank you for articiating in this exeriment. Please do not to talk to any other articiant until the exeriment is over. 2 Roles and 6 Rounds his exeriment consists of 6 rounds, each of which consists of the same sequence of decisions. his sequence of decisions is exlained in detail below. here are 2 kinds of roles in this exeriment: layer A and layer B. At the beginning of the exeriment you will be randomly assigned to one of these two roles. On the first screen of the exeriment you will see which role you are assigned to. Your role remains the same throughout the exeriment. In your grou there are 4 layers A and 4 layers B. he layers of each role get a number. If you are a layer B your otential interaction artners are the layers A, A2, A3 and A4. In case you are a layer A your otential interaction artners are the layers B, B2, B3 and B4. Attention: he numbers of all layers A are fixed, i.e. the same number always reresents the same erson, e.g. A. But: he numbers of all layers B are not fixed, i.e. the number reresenting a given erson might change (the robability that a number is reresented by the same erson as in the revious round is exactly 25%). All articiants get the same information on the rules of the game, including the costs and ayoffs of both layers. Overview of the Sequence of Decisions in a Round Each round consists of a maximum of 4 decisions which are made consecutively. Decisions, 3 and 4 are made by layer A, decision 2 is made by layer B. Short Overview of the Sequence of Decisions in a Round. Player A chooses one rice for action and one rice for action 2.

63 2. Player B gets to know the rices chosen by the 4 layers A (A to A4). hen layer B decides whether he/she wants to interact with one of the layers A. If not, this round ends for him/her. 3. Each layer A gets to know which layers B decided to interact with him/her. A maximum of all 4 layers B can interact with a articular layer A. hen each layer A is informed about the tyes of all layers B who decided to interact with him/her. here are two ossible tyes of layer B: he/she is of either tye or tye 2. his tye is not necessarily identical for all layers B. Player A has to choose an action for each layer interacting with him: either action or action Player B has to ay the rice secified by his/her layer A in decision for the action chosen by his/her layer A in decision 3. Detailed Illustration of the Decisions and heir Consequences Regarding Payoffs Decision In case of an interaction each layer A has to choose between 2 actions (action and action 2) at decision 3. Each chosen action causes costs which are as follows: Action costs layer A 2 oints (= currency of the exeriment). Action 2 costs layer A 6 oints. Player A can charge rices for these actions from all those layers B who decide to interact with him/her. At decision each Player A has to set the rices for both actions. Only (strictly) ositive integer numbers are ossible, i.e., only, 2, 3, 4, 5, 6, 7, 8, 9, and are valid rices. Note that the rice for action must not exceed the rice for action 2. 2

64 Decision 2 Player B gets to know the rices set by each of the four layers A for the two actions at decision. hen layer B decides whether he/she wants to interact with one of the layers A and (if he/she wants to do so) with which one. If he/she wants to do so, layer A can choose an action at decision 3 and charge a rice for that action at decision 4 (see below). If he/she doesn t want to interact, this round ends for this layer B and he/she gets a ayoff of.6 oints for this round. In case none of the layers B wants to interact with a certain layer A, this layer A gets a ayoff of.6 oints for this round as well. Below is an exemlary screen which shows decision 2. In case you wish to interact with a certain layer A lease click Ja (Yes) in the corresonding column and confirm your entry by clicking OK (you don t have to click Nein (No) for the other layers A). If you don t want any interaction at all, you just have to click OK (you don t have to click Nein for all layers A). See exlanation on the screen. In the lower half of the screen you can see all revious rounds (on the exemlary screen round 5 is ongoing). he columns are defined as follows: - Runde : he round, in which something haened - Interaktion : Shows if you had an interaction with a layer A (here: rounds 2-4) - Verbindung zu : Shows with which layer A you interacted (here: in rounds 2 and 4 with layer A4) - Preis für Aktion : Price which was set by layer A for action (in case you didn t have an interaction this field shows -, like here in round ) - Preis für Aktion 2 : Price which was set by layer A for action 2 - Rundengewinn : Your earnings in each articular round denoted in oints (the calculation is exlained below) 3

65 he first number denotes the rice for action ; the second number denotes the rice for action 2 Ja can be activated for a maximum of one column. If you do not activate anything and confirm by clicking OK you will not interact in this round. Decision 3 Before decision 3 is made (in case layer B chose Yes at decision 2) a tye is randomly assigned to layer B. Player B can be one of the two tyes: tye or tye 2. his tye is determined for each layer B in each new round. he determination is random and indeendent of the other layers tyes. With a robability of 5% layer B is of tye, and with a robability of 5% he/she is of tye 2. Imagine that a coin is tossed for each layer B in each round. If the result is e.g. heads, layer B is of tye, if the result is tails he/she is of tye 2. Every layer A gets to know the tyes of all layers B who interact with him/her before he makes his decision 3. hen layer A chooses an action for each layer B, either action or action 2. In case he interacts with more than one layer B these actions are allowed to differ. here are two ossibilities a layer A can have during choosing his action: a) In case layer B is a tye layer, layer A can chose either action or action 2. b) In case layer B is a tye 2 layer, layer A has to choose action 2. At no time layer B will be informed whether he/she is of tye or a tye 2 layer. Player B will also not be informed about the total number of layers B layer A interacted with. Below there is an exemlary screen which shows decision 3. Player A gets to know which of the 4 layers B decided to interact with him and which didn t (first row). If a layer B 4

66 interacts with the layer A under consideration then the tye of layer B is dislayed in the corresonding column. he two rices which layer A set at his decision are shown. he last row has to be filled out for each layer who agreed to interact (the row Interaktion shows JA (Yes)). For each of these interacting layers B an action has to be chosen ( or 2). On the exemlary screen the layers B and B2 decided to interact with layer A, hence layer A needs to enter the actions for these layers (i.e. relace the ). At columns dislaying JA the last row has to be filled in. Below, the row Eigenschaften von Sieler B shows the tyes of all interacting layers B. You cannot change the last row of columns showing NEIN (No). Decision 4 Player A charges the rice (which he determined at decision ) for the action he chose at his decision 3 from each layer B. 5