CALIFORNIA INSTITUTE OF TECHNOLOGY

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1 VSON OF THE HUMANTES AN SOCAL SCENCES CALFORNA NSTTUTE OF TECHNOLOGY PASAENA, CALFORNA COSTLY OFFERS AN THE EQULBRATON PROPERTES OF THE MULTPLE UNT OUBLE AUCTON UNER CONTONS OF UNPRECTABLE SHFTS OF EMAN AN SUPPLY Julian C. Jamison Massahusetts nstitute of Tehnology Charles R. Plott California nstitute of Tehnology SOCAL SCENCE WORKNG PAPER 906 Otober 1994

2 Costly Offers and the Equilibration Properties of the Multiple Unit ouble Aution Under Conditions of Unpreditable Shifts of emand and Supply Julian C. Jamison Charles R. Plott Abstrat The paper reports on the behavior of markets in whih a transations ost is imposed in the form of a tax on bids and asks that are tendered in the market. That is, in the markets studied ommuniation with the other side of the market was ostly. The markets were nonstationary in the sense that market demand and market supply shifted unpreditably eah period and the markets were organize<lby the omputerized Multiple Unit ouble Aution. The results are as follow. (1) A market equilibration proess is observed aross the periods of nonstationary markets. (2) The imposition of the ost on offers did not negate the,tendeny toward market equilibration but the prie disovery proess was "inomplete" relative to the free offer ase. (3) Prie equilibration with the offer ost was slower and effiienies were redued.

3 Costly Offers and the Equilibration Properties of the Multiple Unit ouble Aution Under Conditions of Unpreditable Shifts of emand and Supply Julian C. Jamison Charles R. Plott NTROUCTON The primary fous of this study is the effet of a transation ost on the equilibration properties of an otherwise ompetitive market. oes the existene of a transation ost prevent onvergene? oes it neessarily ause a hange of the prie to whih the system onverges? Theoretially the answer is yes if the transation ost is suffiiently high or possibly if the transation ost is embedded in the market institutions or organization in a manner that alters the nature of the game. However, if the transation ost is not suffiiently high to prevent marginal trades and if the market is of a form that readily "disovers" the ompetitive equilibrium prie, the answer is unknown even theoretially. n part, the open question stems from the fat that we have no solid theory about the prie disovery proess of markets and the onvergene features of market equilibration. This study poses the question for the multiple unit double aution with a hope that the data will reveal some insights about the proess with whih the ompetitive prie is disovered within this form of organization. The multiple unit double aution organization is a natural mehanism for whih the study of transatfons osts an be posed. This partiular mehanism has some of the major features of almost all other mehanisms. t is known that the evolution of prie to the ompetitive equilibrium ours with great reliability. Gains from trade beome exhausted. Furthermore, modem experimental tehnology failitates a detailed study of its operation and the mediums through whih the onsequenes of ostly offers might beome manifest. The organization of the researh is to reate a series of multiple unit double aution markets that are idential in every respet exept for the partiular subjets that are 1 A speial aknowledgment is due to the National Siene Foundation and to the Calteh Laboratory for Experimental Eonomis and Politial Siene for funding support that made these experiments possible. This paper evolved from a projet originating in the Calteh seminar on experimental eonomis. The omments of the students in the seminar have been espeially helpful. We wish to thank graduate students John Keeling and Tanya Rosenblat of M..T., and undergraduate Theodore L. Turoy of Calteh, for their help with the statistial omputations. 1

4 partiipating and whether or not a ost is imposed on the proess of making ontrats. n partiular, in some experiments bids, asks and ontrats are freely tendered and exeuted without the imposition of any ost other than perhaps the subjetive ost that aompanies the pressing of omputer keys and devoting attention to the sreens to proess any information that might exist in the market. n other experiments a ost of making an offer was imposed. That is, any agent that tendered a bid was required to pay a ost of taking the ation. Likewise any agent that tendered an ask was required to pay a ost of taking the ation. Aepting the ask of a seller that had paid the ost of making the ask imposed no ost on the buyer. Likewise aepting a bid that had been tendered by a buyer imposed no ost on the seller. Thus, in the ostly offer ondition a ost was imposed on any agent that made the offer but no ost was involved in aepting an offer. So the ost was not on the transation itself but on making an offer that lead to the transation. n the free offer ondition no ost was imposed on any bid, ask or the aeptane of a bid or ask. The markets under onsideration involved a shift of demand and supply (up or down) eah period by non-onstant amounts. Thus the prie in any one period gave no indiation of the prie that might exist the next period. Furthermore, the redemption values and osts of eah individual hanged eah period so the sheets of inentives given an individual ould not be used to obtain information easily about what the ompetitive equilibrium prie might be for the period. Thus the markets under onsideration did not have the stationary property that is often studied and within whih equilibration is ommonly observed. The study of markets within suh onstantly and unpreditably hanging environments has not been done so that feature of the experiments also offers something new. The experiments thus are an attempt to unover some of the features of the nature of market onvergene and are a step in the investigation of the mystery of the prie disovery proess. Speifially four questions are posed. (1) oes equilibration our in a onstantly hanging environment? f no tendeny exists for equilibration within a period, then learning aross periods may not our and market pries ould wander randomly. (2) oes equilibration our in the presene of an offer ost? Suh equilibration need not our sine the terms of offers in a bargaining proess an be influened by whih party made the bid or ask. Antiipation of the fat that the other side might not want to bear the ost of another round of bidding might indue parties to offer on more self serving terms. Pries ould therefore gyrate depending upon whih side made the offer. (3) f equilibration ours, are the equilibrium magnitudes themselves influened by the existene of the ostly offer? The magnitudes are pries, volumes and effiienies. Sine the preditions of game theory an differ from demand and supply models, one might even expet that the equilibration be at something other than a ompetitive equilibrium. (4) s the speed of equilibration influened by the ostly offer? The paper is organized into four setions, inluding this introdution. The seond setion ontains the parameters and experimental design. Sine the operations of the multiple unit 2

5 double aution are well known very little spae is devoted to a desription of the institution or the assoiated experimental setting. The third setion is a brief disussion of the ompetitive model and some of the relevant behavioral properties of markets. The fourth setion ontains the major results and the final setion ontains a summary of onlusions. EXPERMENTAL ESGN AN PARAMETERS The general struture of the experiments is ontained in Table 1. All parameters, inluding the time within eah period, were maintained identially aross six experiments. Eah of the six experiments onsisted of a double aution market mehanism, with three buyers and three sellers. The redemption values and osts were symmetri. The magnitudes for the parameters used during the first period of any experiment are ontained in Figure 1. Eah experiment had ten periods after the first period, exept the first experiment, whih had twelve periods. Subjets were students and staff from the California nstitute of Tehnology who had previous experiene in the operation of omputerized MUA markets but had no experiene with the parameters or proedures of the experiments reported here. There were three types of buyers and sellers, one of eah in eah period. The assignment of values to eah of the buyer and seller types for period one of an experiment are in Figure 1. The atual table of numbers, the redemption values for buyers and osts for sellers, for eah type and for period one are in Table 2-a. The individual subjets rotated among type. For example, a subjet who was type 3 in period 2 beame type 1 in pe1iod 3, type 2 in period 4 and was again type 3 in period 5. The individual shedules eah period differed by a onstant amount that is listed at the bottom of Table 2-b. For example, to get the shedules for all types in period 2 add a onstant of -40 to the values of eah entry of eah shedule. The onstant listed in Table 2-b is - 40 so the differene between periods one and two is that in period two eah of the shedules is shifted downward by 40. n order to alulate the shedules for period 3 the onstant of -200 must be added to eah of the values that were omputed for period 1, et. Thus, the hanges in values and rotation that ourred eah period made it very diffiult for an individual to detet the nature of the general hanges in demand and supply from the information on the inentive sheet. However, lose examination and a omparison of periods would have revealed muh. The sheets were presented in a manner that prevented an individual partiipating in any one period from knowing what the next period inentive parameter values might be. However, past parameters of an individual were available to that individual, whih, if studied arefully, would ontain information. Our belief is that these relationships went unnotied by subjets. For three of the six experiments, a ost of offering was introdued. This was a ost of 10 frans (generally about $0.25) for eah bid or ask, i.e. eah offer made in the market. The aeptane of a bid or ask did not inur the ost, nor was there any additional ost if quantities larger than one were offered. These ostly offers are analogous to harging a 3

6 fee for market entry, advertising ost for reahing a buyer or for modeling transportation osts of getting units to or from the market. Subjets were randomly assigned to be either a buyer or seller and to a seat at a omputer. Eah had an idential instrution sheet (see the Appendix). The instrutions were passed out and then read aloud. Subjets in the ostly offer ondition had a box on their inentive sheet that said "postings" and were told to put a mark for eah time they submitted a bid or ask whih was aepted by the market. Bids or asks for multiple units ounted only as one offer. At the end of eah period subjets were to ount their total number of offers and mark this on the sheet, subtrating 10 frans for eah offer from their profit Subsequent heks of the data verified the auray of these reordings. All subjets were familiar with the basi market operation, so only a single pratie period was neessary. After this pratie session subjets were told that they were making deisions for atual money, and this ontinued for ten periods, with small breaks in between for aounting purposes. No subjet knew that the experiment would last only ten periods until the last period was ompleted, at whih time they were told to ompute their total profits. MOELS AN BEHAVORAL PROPERTES The demand and supply and resulting ompetitive equilib1ium for the first period of eah experiment are in Figure 1. The demand and supply urves were shifted eah period by a onstant and as a result the ompetitive equilibrium pries differed eah period and are produed in Table 3. A theoretial ompetitive equilibrium volume of nine units was the same aross all periods and experiments. Whether or not the market will "disover" the equilibrium prie eah period under onditions of unantiipated shifts of demand and supply is substantially unknown. The equilibration properties of onstantly shifting markets have been studied but in previous studies the shifting properties themselves had a onstant property. For example aniels and Plott (1988) studied markets in whih the demand shifted up eah period by a onstant perentage. Williams (1979) studied demands and supplies that had a onstant ylial behavior. n both ases the data suggest that markets onverge to suh "moving targets" but the ase in whih the target has little preditability from the past has not been studied. The onsequenes of one time shifts in markets has been often studied but the onstantly shifting markets studied here is new. Thus, the data from the experiments with free offers will add new information about the onvergene apaities of markets. The existene of influenes of ertain types of transations osts in experimental markets in well known and doumented. Plott and Smith (1978) demonstrated that a natural transations ost exists in experimental markets that an easily influene the volume omponent of an equilibrium. f agents are given no ommission for trades and if the demand limit prie for the marginal unit is exatly equal to the supply limit prie of the marginal unit of supply, then these two units tend not to trade. The transation ost an 4

7 be seen as restriting volume. The existene and impliations of this natural transation ost and ertain undesirable properties of ommissions to overome it, lead to the use of parameters with an equilibrium "tunnel" property. The limit prie of the marginal demander is typially stritly higher than the limit prie of the marginal supplier so the possibility of stritly positive gains from trade exist at the margin. Refer again to the demand and supply model in Figure 1. As disussed above the magnitudes were for period one parameters. As an be seen there is a "tunnel" twenty frans wide for the last two units, before supply and demand rossed. Thus, stritly speaking all pries in the range of the tunnel are equilibria. For purposes of disussion it is easy to disuss THE equilibrium and for this purpose the average prie of the equilibria is used. That is, when the disussion refers to THE equilibrium prie, the referene is to the middle of the tunnel. The equilibrium pries listed in Table 3 are these numbers. As was mentioned above, the tunnel is ustomary beause it is known that marginal units do not trade without some sort of reward. The pa1tiular "tunnel" represented by the parameters of the experiments and ontained in Figure 1, is rather large given ordinary beliefs about subjetive transation osts. n the experiments to be studied here the gains from trade between marginal units are about $0.50 per unit as ompared with the usual $0.05 implemented in experimental markets. The size of this "tunnel" means that even with the ost of offering of 10 frans or about $0.25, there were pries that made a profit for both buyer and seller at every unit up to the ompetitive equilibrium quantity. Thus, even with the ostly offers there were always gains from trade over a prie range of about $0.25, whih is well above what is ordinarily believed to be subjetive transation ost. After having looked at the data, aspets of theory emerged that might be helpful in understanding what is observed in the onvergene proesses. These are regularities in the data that are understandable from a speial theoretial point of view. n order to emphasize their importane we will refer to them as priniples. This disussion has emerged after we studied the markets so the design annot be onstrued as an attempt to test the ideas in some systemati way. Nevertheless, it is easier to disuss the ideas now, during a disussion of the models rather than later. The behavior of the double aution in general, without ostly offers, seems to onform to a PRNCPLE OF SUCCESSFUL PRCE SCOVERY. That means that during the operation of a market the pries at whih trades an take plae beome widely known. All buyers know a range of pries that is learly out of bounds beause the sellers annot or will not take less. Similarly sellers have a similar idea about what buyers are willing to take. Under suh irumstanes the plaing of an order that is a likely andidate for exeution is not a partiularly diffiult or artful task. n a sense the set of mutually benefiial net trades beomes publi information. The path-breaking paper of Easley and Ledyard (1993) axiomatize a behavioral quality that an lead to suh a property. They postulate that as the end of a period draws near, a tendeny exists for individuals to reveal their limit pries in their offers. That is, for Easley and Ledyard the priniple of suessful prie disovery operates through a PRNCPLE OF FULL REVELATON. 5

8 The double aution has another property that was partially aptured by an Easley and Ledyard axiom. For lak of a better term we will all it the PRNCPLE OF MMEATE ACCEPTANCE. As a period grows near the end, a tendeny exists for individuals to aept whatever offer exists in the market if the offer is profitable for them. They wish to aept the terms immediately while the offer lasts and before the period ends. Together the two priniples apture muh of the nature of the trading proess. The area of gains from trade beomes known, espeially near the end of a period. Furthermore, it beomes easier to tender offers that will be aepted as the priniple of immediate aeptane takes over. No individual will fail to trade beause of strategi reasons. Thus all gains form trade will be exhausted and the market volume will be at the ompetitive equilibrium quantity. RESULTS Figures 2 and 3 ontain examples of the time series of ontrat pries for experiments with free offers (Figure 2, Experiment 0524) and with ostly offers (Figure 3, Experiment 0217). The vertial lines indiate the different periods. The horizontal lines indiate the ompetitive equilibrium prie for eah period as alulated from parameters. The visual impression taken from these figures is that onvergene ours under both onditions but it is faster and more aurate under the ondition of free offers as opposed to the ondition of ostly offers. The onlusions below will make that impression preise. The first result is that onvergene to the ompetitive equilibrium is ourring within eah period even with the parameters shifting. nterestingly enough, in this ase of unpreditable shifts the onvergene to the ompetitive equilibrium does seem to improve with experiene in the market. This ours under onditions of free offers and also under onditions of ostly offers. RESULT 1. Under both onditions of free offers and ostly offers the within period onvergene of ontrat pries is to the equilibrium. Furthermore, there are slight improvements over time. SUPPORT. The analysis will proeed by an examination of the ase of free offers, and then will fous on the ostly offer ase. Table 4 ontains the results of the estimation of the Ashenfelter/El-Gamai 2 model of market onvergene. Pit - P eq it =Li i Bli 1/t + B2 (t-1)/t + eit Where i is the experiment and t is the period. Pit is the average prie of a ontrat in period t of experiment i. i takes value 1 if the experiment is i and zero otherwise. P eq it 2 This model was first used in Noussair, Riezman and Plott (forthoming) and resulted from disussions with and suggestions of Orley Ashenfelter and Mahmoud El-Gamal. 6

9 is the equilibrium prie (the midpoint of a range) predited by the ompetitive model in period t of experiment i. The etor term is assumed to be normal with 0 mean and onstant variane. The Table ontains the results of estimation for the two data sets. The oeffiient B2 is an estimate of the asymptoti behavior of the time series that is to be ompared with the equilibrium preditions of the ompetitive model. Given the parameters of the model, there is a "window" of 20 frans or equilibrium &ries. P eq is the midpoint of this window. Thus pries of 10 frans on either side of P e are still equilibria. For the ase of free offers B2 is estimated to be 9.7 frans whih is approximately 20 ents. This is within the 10 fran differene that is allowed by the non-uniqueness of the equilibrium pries. Thus we an onlude that experiments with free offers are onverging to the equilibrium pries. A omparison of the data in the initial periods, the B 1i terms, further supports the onlusion of onvergene. These terms estimate the initial starting points of the ontrat pries during the first period of the experiment. As an be seen two of the three experiment's prie levels during the first periods were outside the equilibrium prie range. Volumes are reported in Table 5 and as an be determined by inspetion the equilibrium volume of 9 was attained in eighty perent of the periods. The results of the experiments with ostly offers are similar. As an be seen from an examination of Table 4 the estimate of B2 is whih is not signifiantly different from zero. Thus the onvergene of these markets is to the ompetitive equilibrium prie. An examination of the B 1i terms demonstrates that the pries in the initial periods of two of the three experiments are outside the equilibrium prie range. The volumes in Table 5 are at the ompetitive equilibrium level of 9 units in seventeen perent of the periods (as opposed to eighty perent for the free offer ondition). This divergene of the volume from the model will be disussed in detail later. The data presented above might lead to the impression that the ostly offer markets are atually onverging faster than are the free offer markets. The B2 term for the ostly offer ase is almost zero, the middle of the ompetitive equilibria, whereas the measurement for the free offer ase is nearer the boundary of the equilibria. The next result demonstrates that suh an impression is not mtet. The free offer markets onverge more rapidly and are more effiient. The apparent relative suess of the ostly offer markets is probably due to the aident of the pattern of first period pries and the nature of the averaging proess impliit in the statistial model. The next result summarizes some of the major effets of the ostly offer on market performane. RESULT 2. The imposition of a ost of offers lowers market effiieny, redues volume and redues the speed of onvergene to the ompetitive equilibrium. SUPPORT. The properties of the data will be explored in the order of effiieny, volume and speed. The effiienies of eah period of eah experiment are ontained in Table 6. On average the effiieny of the free offer experiments is 97.2% and on average the 7

10 effiieny level of the ostly offer experiments is 91.9 %. Notie that the average effiieny of the free offer experiments is heavily influened by one period of one experiment (t might have been due to a typo of a type that sometimes our in eletroni markets.). f this one period is removed from the data then the effiieny of the free offer ase is on average 99.1 %. With or without the "outlier" a test of a differene in effiieny levels between the two treatment onditions (free offer or ostly offer) leads to a rejetion of the hypothesis of equal means at the 0.02 level with the "outlier" and at the 0.01 level without it. The markets with ostly offers operated less effiiently than did the markets with free offers. Table 5 ontains the volume in eah period of eah experiment. The ompetitive equilibrium volume should be nine units in any given period. The volume in the free offer experiments is on average 9.1 per period. The volume in the ostly offer experiments is on average 7.8 per period. The hypothesis of equality an be rejeted at the.01 level Sine the average volume of the free offer ase is above the average volume in the ostly offer ase we onlude that the impat of the ostly offer is to lower volume. Speed of onvergene is measured by the following model. P.. p eq.., rv - Pt+.. ]t 1J = -..,,, e J t The variable Pijt is the t th ontrat that ourred in period j of experiment i. The variable P eq ij is the ompetitive equilibrium prie that prevailed during that period of the experiment. The use of the absolute value is used to measure the distane from the equilibrium and the form of the model implies that if the diretion is toward the equilibrium on average then in the limit the differene will be zero. The p term measures the speed of onvergene. f it is positive then the system is going toward zero and if it is large and positive then it is moving quikly toward zero. The omparison of speed of onvergene is thus made with the omparison of p in the different experiments. The estimated oeffiients of the model are ontained in Table 7. For the free offer ase the P is estimated to be 0.12 and for the ostly offer ase the estimate is Thus the speed of onvergene in the free offer ase is greater. The onfidene in the differene is approximately The next 2 results form the basis of onjetures about the mehanism through whih the effets of the imposition of offer osts beome manifest. Figures 4 and 5 ontain a time series of offers for the two onditions of free offers and ostly offers respetively. The ontrats are omitted so only the patterns of bids and asks remain. The figures give two impressions. First the number of offers is muh greater under the onditions of free offers. Seondly the "bargaining" ativity in terms of new bids and asks ontinues with a flurry until the very end of the market period in the free offer ase. On the other hand the density of ativity in terms of bids and asks at the final moments of a period are muh fewer when ostly offers are imposed. The next two results make those impressions preise. 8

11 RESULT 3. The imposition of an offer ost redues the number of offers and inreases the quantity tendered in any given offer. However, the average size of a ontrat is not influened by the existene of ostly offers. SUPPORT. Table 8 ontains for eah period of eah experiment the number of offers (the number of bids plus the number of asks in a period),the average quantity offered and the average size of a ontrat eah period. n the free offer ase there are on average 51 offers per period. n the ostly offer ase there were on average 9. The differene in numbers of offers is dramati in magnitude and signifiant at the 0.01 level. The number of offers falls with the imposition of the ost of offers. The table also ontains the average size of offers whih is 1.2 in the ase of the free offer and is 1.9 in the ase of the ostly offers. The size of offers is signifiantly greater ( 0.01 level of signifiane) in the ostly offer ase than the free offer ase. As an be seen in the table the average size of ontrats is almost uniformly 1 in all ases (on average the size of ontrats is 1.02 in the free offer ase and 1.03 in the ostly offer ase). RESULT 4. The time left in the period at the last transation inreases as a result of the imposition of the ostly offer and the number of offers after the last ontrat dereases as a result of the imposition of ostly offers. SUPPORT. Table 9 reports the differene in the time at whih the last ontrat was made in a pedod and the time at whih the period ended. The table also reports the number of offers that were made after the last ontrat. As an be seen from examination of the table the average time remaining after the last ontrat was 21.1 seonds in the ase of the free offer experiments and was on average 73.5 seonds in the experiments with the ostly offer. The differene is signifiant at the 0.01 level. The number of offers that ourred after the last ontrat was on average 2.8 in the ase of free offers and it was on average 0.7 in the ase of the ostly offers. Again the differene is signifiant at the 0.01 level. Thus the imposition of ostly offers had the effet of inreasing the amount of time between the ourrene of the last transation and the end of the period and also dereasing the number of offers after the last transation was made. OBSERVATON: n both the ases of free offers and ostly offers onditions, at the end of the period profitable trades are not possible at the pries that are offered. SUPPORT. The observation is true of all periods of all experiments with the exeptions of period two of experiment 0524 and period 8 of experiment However, in these two ases the offer was made only within the final three and two seonds of the period respetively, so even in these two ases the observation tends to hold beause there was, pratially speaking, too little time remaining in the period to aept. There are many ases in whih offers that would have left zero profits for the aepting party were left on the table, whih is typial of the subjetive transation ost disovered by Plott and 9

12 Smith. CONJECTURE: The ostly offer indues an inomplete prie disovery proess. The priniple of suessful prie disove1y is never fully operating. The priniple of immediate aeptane is operative but the priniple of full revelation is not operating. The story that supports the onjeture is a straight-forward reounting of the results listed above. n the absene of ostly offers, onvergene to the ompetitive equilibrium prie and quantity an be expeted. n addition the system will operate at near 100% effiieny. The imposition of ostly offers failitates a general fall in the level of effiieny. Gains from trade are left on the table. This tendeny to walk away from gains from trade is not due to an (perhaps strategi) unwillingness to trade. The ost on offers results in a redution in the number of offers (but not the willingness to trade at a given prie). t also redues the propensity for offers to be enouraged by the approah of the end of the period. n other words, the Easley and Ledyard priniple of full revelation is not at work. At least two different models an be used to explain any redution in limit prie revelation. The first might be a simple searh model that postulated an additional ost on searh will redue the amount of searh in terms of offers that are made. A redution in the number of offers is a redution in the ompleteness of the prie disove1y proess. The seond has more of a bargaining flavor whih has the two individuals engaged in a prisoner's dilemma over whih one will bear the ost and tender the offer. The result is an offer by neither. The onjeture above impliitly suggests that the phenomena of inomplete prie disovery is due to the foimer mehanism. SCUSSON AN CONCLUSONS This study was motivated by a series of questions the answers to whih an now be summarized. First, the prie disovery proess typial of stationary markets extends itself to markets with no stationary properties. This is a partiularly interesting result beause it suggests that onvergene to an equilibrium is due in part to what might be learned (or oordinated) with the partiular individuals in the market in addition to knowledge about the partiular parameters that might be present in the environment. This onlusion is partiularly interesting beause learning is generally thought to involve only information about environmental parameters and not about the omplexities that might aompany partiular individuals or individuals as a group. t ould be said that the equilibration properties observed are due to the fat that the ompetitive equilibrium was an "easy shot". That is, the equilibrium range was wide and the volumes were small relative to environments in whih auray is ordinarily studied. The equilibrium "window" was $0.50 as opposed to $0.20 that is frequently used. To this ritiism we have no real reply. t is not exatly obvious how to translate the ritiism into 10

13 a program of experimentation without additional theory to guide the effort. To this end some speulations about theory are inluded at the end of the setion of results. The seond question posed was related to the impat of ostly offers. The existene of ostly offers does not negate the tendeny for the prie to equilibrate. Gyrations, breakdown of trade, or other extreme phenomena were not observed. The pries tended to equilibrate at a level near the ompetitive equilibrium. By omparison with the free offer ase, the prie onvergene proess was slower and the market effiieny was lower in the ostly offer ase. These questions of omparative performane were the third and fourth questions initially posed and are now answered. n addition, a type of paradox presents itself. f pries under the ostly offer onditions onverge to the ompetitive equilibrium how an it be that ostly offers produe market ineffiienies? A onjeture is offered in the results setion as a solution to the paradox. The onjeture is that the ase of ostly offers is one of inomplete prie disovery fostered by the redued searh. The ost of offers redues the number of offers and as a result, the ability of buyers and sellers to find eah other is hampered. Even though the pries are in the range of the ompetitive equilibrium, this fat is not known to the agents who refrain from making offers for fear of "missing" the area of gains from trade and thereby suffering the offer ost with no offsetting gain. Thus, the onjeture has roots in an intuitive theory that is aptured by the Easley and Ledyard model of the onvergene proess and thereby supports that model as entral to an understanding of the prie disovery proess. Speifially, the imposition of the offer ost auses violations of the Easily and Ledyard axiom that we have named the Priniple of Full Revelation, and aordingly, the ineffiienies are fostered by a redution of information in the market. REFERENCES aniels, B. P. and C. R. Plott, "nflation and Expetations in Experimental Markets," Bounded Rational Behavior in Experimental Games and Markets, edited by R. Tietz, W. Albers, and R. Selten. Berlin Heidelberg: Springer-Verlag, Easley,. and J. 0. Ledyard, "Theories of Prie Formation and Exhange in ouble Oral Autions," The ouble Aution Market: nstitutions, Theories and Evidene, edited by. Friedman, J. Geanakoplos,. Lane, and J. Rust. Santa Fe nstitute Studies in the Sienes of Complexity, Proeedings Volume XV., Addison-Wesley, Plott, C. R. and V. L. Smith, "An Experimental Examination of Two Exhange nstitutions," The Review of Eonomi Studies, Volume. XLV (1) (February 1978): Williams, A. W., "ntertemporal Competitive Equilibrium: On Further Experimental Results," Researh in Experimental Eonomis, Vol.1, edited by V. L. Smith. Greenwih, Connetiut. JA Press, (1979):

14 Noussair, C. N., C. R. Plott, and R. G. Riezrnan, "An Expeiirnental nvestigation of the Patterns of ntemational Trade," Soial Siene Working Paper no. 799, Pasadena: California nstitute of Tehnology. Revised August Forthoming in Amerian Eonomi Review. 12

15 APPENX A The instrutions for both treatments are ontained below. The ostly offer ondition differed from the free offer ondition only by the insertion of the sentenes in the brakets [ ]. GENERAL NSTRUCTONS This is an experiment in the eonomis of market deision making. The instrutions are simple and if you follow them arefully and make good deisions you might earn money whih will be paid to you in ash n this experiment we are going to ondut a market in whih some of you will be buyers and some of you will be sellers in a sequene of market days or trading periods. Enlosed with the instrutions you will find a sheet labeled Buyer or Seller, whih desribes the value to you of any deisions you might make. You are not to reveal this information to anyone. t is your own private information. The urreny in these markets is frans. Eah fran is worth dollars to you. SPECFC NSTRUCTONS TO BUYERS uring eah market period you are free to purhase from any seller or sellers as many units as you might want. For the first unit that you are buying during a trading period you will reeive the amount listed in row (1) marked Redemption Value under Unit Number 1: if you buy a seond unit you will reeive the additional amount listed in row (4) marked Redemption Value under Unit Number 2, et. The profits from eah purhase (whih are yours to keep) are omputed by taking the differene between the redemption value and transation ost, or purhase prie, of the unit bought. That is, [your earnings= (redemption value) - (transation ost)]. Suppose, for example, that you buy two units and that your redemption value for the first unit is 200 and for the seond unit is 180. f you pay 150 for your first unit and 160 for the seond unit, your earnings are: earnings from first = = 50 earnings from seond = = 20 total earnings = = 70 The blanks on the table will help you reord your profits. The purhase prie of the first unit you buy during the first period should be reorded on row (2) at the time of 13

16 purhase. You should then reord the profits on this purhase as direted on row (3). [At the end of the period reord your total number of postings, find the posting fee as direted, and reord your total profits on the last row on the page]. Subsequent periods should be reorded similarly. SPECFC NSTRUCTONS TO SELLERS uring eah market period you are free to sell to any buyer or buyers as many units as you might want. The first unit that you sell during- a trading- period you obtain at a ost of the amount listed on the enlosed sheet in row (2) marked Buybak Cost under Unit Number l; if you sell a seond unit you inur the additional ost listed in row (5) marked Buybak Cost under Unit Number 2, et. The profits from eah sale (whih are yours to keep) are omputed by taking the differene between the transation revenue, or prie at whih you sold the unit, and the ost of the unit. That is, [your earnings= (transation revenue) - (buybak ost)]. Suppose, for example, your buybak ost of the first unit is 140 and your ost of ti} seond unit is 160. For illustrative purposes we will onsider only a two-unit ase. f you sell the first unit at 200 and the seond unit at 190, your earnings are: earnings from first = = 60 earnings from seond = = 30 total earnings = = 90 The blanks on the table will help you reord your profits. The sale prie of the first unit you sell during the first period should be reorded on row (1) at the time of sale. You should then reord the profits on this sale as direted on row (3). [At the end of the period reord your total number of postings, find the posting fee as direted], and reord your total profits on the last row on the page. Subsequent periods should be reorded similarly. 14

17 Transation Reord for Buyer#_ Period 1 Unit Number Redemption Value } ''''""" ; r.. Q.. Q L ! 3 Profit (line 1-2) Unit Number 2 l g!!.1.p.j!q!.j:.y.aj f 5 Transation Cost Postings !?.f..rn..4.. }> ,.... ::; "i <l j;1i Unit Number 3.. v Transation Cost )o ooo unouo oo oooooooooo 1 9 Profit (line 7-8) )...!'!:9.n.(.. J9...J L Unit Number 5 } Redemption Value l.. i1... i i Vi: fa)... Unit Number 6 L... J9.... g.!!.1.p Y f 17 Transation Cost 1...!....!?.f. t.m.}9... :J7.L : Unit Number 7! 19 Redemption Value 1 20 Transation Cost > i 21 Profit (line 19-20) , Unit Number 8 L Transation Cost... P. i!?!.!..y !.....?....!'!:9.f HY ? Unit Number 9 } Redemption Value L.....?.... g.q..p..!.9... Y Transation Cost... J f.tJF..}?...:..?. L......!....?.J.... $.....Rr.9.n..n.. }.:±-.... ±.2..±..::: L...}... Nµ,.!!.1.!?. r..2.lp.9. g.. Q?.9. L Posting Fee (line 32 x ) 15

18 Table 1 Experiments and Conditions Experiment Condition Loation Experiene Number Number of Subjets of Subjets of Periods Costly CT General 6 12 Offer Experiened Costly CT General 6 10 Off er Experiened Free CT General 6 10 Offer Experiened Free CT General 6 10 Offer Experiened Free CT General 6 10 Offer Experiened * Costly CT General 6 10 Offer Experiened *This experiment was interrupted briefly by a omputer shutdown 16

19 Table 2-a Period 1 Redemption Values and Costs by Subjet Type Buyer Redemption Values Seller Costs u

20 Table 2-b Amount Added to Entries in Table 2-a to Obtain Corresponding Shedules for All Periods Period Amount Added f-1 00

21 Table 3 Expeted Equilibrium Pries By Period Period Prie (Pratie) * * 145 *First experiment only 19

22 Table 4 Estimated Parameters for theashenfelter /El-Gamal Model - Free Offer: B,, B,, B,, B Competitive Equilibrium Predition Estimated Coeffiient Standard Error Number of Observations Correted r rho Costly Offer: B,, B,, B,. B, Competitive Equilibrium Predition Estimated Coeffiient Standard Error Number of Observations Correted r rho

23 Table 5 Volumes by Period Experiment Period Free Offer Costly Offer * Average *Suspeted type 21

24 Table 6 Effiienies by Period Experiment Period Free Offer Costly Offer 1 100% % 97.3% 89.2% 91.9% 82.4% 2 100% 91.9% 93.9% 84.5% 93.2% 86.5% 4 100% 100% 100% 97.3% 97.3% 97.3% 5 100% 100% 100% 97.3% 85.1% 100% % 100% 100% 97.3% 91.9% 82.4% 7 100% 100% 100% 97.3% 94.6% 77.0% 8 100% 97.3% 100% 82.4% 86.5% 97.3% % 100% 100% 97.3% 100% 97.3% Average 97.2% 91.9% *Suspeted typo 22

25 Table 7 Estimated Parameters for Speed of Convergene P.. - Pq.. = ae- 1+e Jt J Free Offer: Competitive Equilibrium Predition Estimated Coeffiient Standard Error * B Number of Observations Correted r 2 rho Costly Offer: Competitive Equilibrium Predition Estimated Coeffiient Standard Error * B Number of Observations Correted r 2 rho *Atually the standard error is 0.14 out of n 17.2 = out of n 13.3 =

26 Table 8 Number of Offers, Average Quantity Offered, and Average Contrat Size by Period Experiment Period ,1.0,1.0 64,1.1,1.l 2. 54,1.1,1.0 74,1.1, ,1.2,1.0 48,1.2, ,1.0,1.0 61,1.3, ,1.1,1.0 57,1.3, ,1.0,1.0 59,1.3, ,1.0,1.0 64,1.1, ,1.0,1.0 61,1.2, ,1.1, , ,1.3,1.0 53,1.3,1.0 Free Offer ,1.4,1.0 45,1.2,1.0 37,1.6,1.0 46,1.3,1.0 48,1.3,1.0 44,1.4,1.0 32,1.3, ,1.5,1.0 38,1.7,1.1 Costly Offer ,1.3,1.0 9,2.7,1.2 8,1.5,1.0 13,1.3,1.1 12,1.8,1.0 10,2.2,1.0 16,1.6,1.1 9,2.3,1.1 6,3.2,1.0 11,1.8,1.1 8,2.1,1.0 6,2.3,1.1 12,1.8,1.0 9,1.6,1.2 5,3.0,1.0 10,1.3,1.0 7,2.1,1.0 5,1.6,1.0 9,1.4,1.0 9,2.4,1.0 4,2.5, ,1.0 7,1.7,1.0 6,2.3,1.0 8,1.8,1.0 8,1.9,1.0 5,2.0,1.0 11,1.5,1.0 5,2.8,1.1 11,1.8,1.0 Average 50.5, 1.2, , 1.9,

27 Table 9 Number of Seonds Remaining and Number of Subsequent Offers for the Last Transation in a Period Experiment Period Free Offer Costly Offer ,1 3,0 9,2 15,2 6,1 15,2 2,0 10,3 60,7 9, ,0 36,4 157,4 2,0 109,18 16,3 17,4 2,1 7,1 1, ,7 59,7 5,1 5,1 14,4 8,2 6,3 2,0 21,3 8, ,0 1,0 124,2 115,1 152,2 57,1 117,2 145,1 174,1 1, ,2 133,3 15,0 52,1 33,1 3,0 51,0 16,0 55,0 1, ,0 9,0 12,0 179,1 165,0 17,0 220,0 48,0 101,1 48,2 Average 21.1 seonds 2.8 offers 73.5 seonds 0.7 offers 25

28 Figure "' : m :i... u. - Q) :i... a emand - Supply 350 L... 0 Quantity 5...,.--;--,...-r--.--,-, :-'--r--r

29 ' Figure 2 Contrat Pries Experiment 0524 with Free Offers Q) CJ ;f 340 r -- \ -v-\ t."' - 1' - \.m. \, J -"' N -...) ' Clok( se)

30 Figure 3 Contrat Pries Experiment 0217 with Free Offers ) t.) o Clok( se)

31 Figure :> '> <> <> "? 1fjr if "o " <> 0. > llfil>.. 8 )'Sit'" " ".:J l t 420 a> u : <>,it:.s': : <;;p <> -$ "$ < :> op Jlll (!J ']; (1 (> <> a" < m6p 0 a b " <j;:'> ;tr,.gdl "', <:. > ".. " p Cl b <> i.< <><> - $a ' d' -1',>. : -{,... r:«:- iii'" '."-. <:= p aa a : a a 8 f:> ' ' < w \! <> <\ :, l>o,f' p Clok( se)

32 Figure e;.-0- < - - ti- - - " " " C " d _,..'9f! " ".,., p i - r:- - - "' :> > - - Fx->..,. Cl.) Q : 0.. >.. <> <> 280 > <> b " - ::>9 -a -:> 141, Clok( se)

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