DEPARTMENT OF ECONOMICS COLLEGE OF BUSINESS AND ECONOMICS UNIVERSITY OF CANTERBURY CHRISTCHURCH, NEW ZEALAND

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1 DEPARTMENT OF ECONOMICS COLLEGE OF BUSINESS AND ECONOMICS UNIVERSITY OF CANTERBURY CHRISTCHURCH, NEW ZEALAND Does Farness of the Outsde Opton Matter? by Maroš Servátka and Radovan Vadovč WORKING PAPER No. 06/2008 Department of Economcs College of Busness and Economcs Unversty of Canterbury Prvate Bag 4800, Chrstchurch New Zealand 1

2 WORKING PAPER No. 06/2008 Does Farness of the Outsde Opton Matter? by Maroš Servátka 1 and Radovan Vadovč 2 Aprl 13, 2008 Abstract: Expermental evdence suggests that the sze of the foregone outsde opton does not affect the behavor of the opponent n a lost wallet and pe sharng games but that t matters n a mn-ultmatum game. In ths paper we expermentally test a conecture that t s the farness property of the outsde opton whch could be responsble for ths effect. We compare the behavor of subects n the lost wallet game when they face a fully unequal ( unfar ) outsde opton,.e., the frst mover gets 10 and the second mover gets nothng, and when they face an equal ( far ) outsde opton,.e., both get an equal amount of 5. Contrary to our conecture we do not fnd a sgnfcant dfference. Keywords: Expermental economcs; Outsde opton; Farness JEL Classfcaton Codes: C72; C78; C91 Acknowledgements: We are grateful to Martn Dufwenberg for helpful dscussons and to SonderForschungsBerech 504 at the Unversty of Mannhem for fnancal support. 1 Department of Economcs, College of Busness and Economcs, Unversty of Canterbury, Prvate Bag 4800, Chrstchurch, New Zealand. 2 Department of Economcs, Insttuto Tecnológco Autónomo de Méxco. E-mal: rvadovc@tam.mx. Author for correspondence: Emal: maros.servatka@canterbury.ac.nz. 2

3 1.1 Introducton The recent expermental studes of Dufwenberg and Gneezy (2000) and Brandts, Güth, and Stehler (2006) have produced qute surprsng and counterntutve results that the sze of foregone outsde opton by the frst mover does not affect the behavor of the second mover n a lost wallet and pe sharng game, respectvely. In fact, several promnent models predct exactly the opposte type of behavor: For example, n the models of recprocty (Falk and Fshbacher (2006) and Dufwenberg and Krschteger (2004)) the frst mover s knder the hgher the outsde opton he foregoes as the potental cost of dong so s hgher. Ths should be suffcent to nduce the second mover to be more recprocal. Smlarly, f the second mover s gult-averse (Battgall and Dufwenberg (2007)), he should beleve that the frst mover expects to receve more the hgher the forgone outsde opton. Ths reasonng s also referred to as the psychologcal forward nducton. The absence of a behavoral effect of the alternatve that has not been chosen s a puzzle. Ths s magnfed by the fact that the same behavor s not observed unformly across games. For example, Charness and Rabn (2002) observe that the second mover s behavor has been nfluenced by the alternatves avalable to the frst mover n a sequental game nvolvng an element of trust, very smlar to the lost wallet and pe sharng games. Smlarly, n a slghtly dfferent expermental settng of a mn-ultmatum game Brandts and Solà (2001), Falk, Fehr, and Fschbacher (2003), Cox and Deck (2005) fnd that the reference pont sgnfcantly affects the behavor of subects, as explaned by negatve recprocty. Brandts et al. (2006) conecture that t s because the outsde opton n ther settng s very unfar as t gves everythng to the frst mover. The same s true for the Dufwenberg and Gneezy (2000) study. In ths paper we explore ths ssue by studyng whether subects behavor responds to the equalty (farness) of the outsde opton. 1.2 Relatve Farness of Outsde Optons Based on Brandts et al. (2006) we conecture that the relatve farness mght play a role n the decson-makng process of the second mover and n partcular when he s consderng the 3

4 outsde opton as a part of hs decson. Consder the lost wallet game n whch the frst mover decdes to ether choose IN, allowng the second mover to splt the surplus between both players; or to choose OUT, collectng the outsde opton. On an ntutve level, f the outsde opton s very unfar towards the second mover, e.g., 10 for the frst mover and 0 for the second mover, then the second mover may dsagree wth such splt and because of t dsregard t entrely. On the other hand, f the outsde opton s far, the second mover conscences to t and s then wllng to spend more tme consderng ts mplcatons. Accordng to our conecture the far outsde optons are ncorporated nto second mover s decson whle unfar outsde optons are gnored. To make ths clearer suppose the outsde opton s x, x, where x and x are both nonnegatve and denote what the frst and the second mover gets on the outsde. Consder now a farness weghtng functon f x, x whch corrects for the mportance that the outsde opton assumes n the mnd of each player. That s, the outsde optons would be perceved as f x x x, f x, x, x. The farness weghtng functon satsfes the followng assumptons: Assumpton 1: 0, x 0 f and f x, x 1. Assumpton 2: f 0 for x x, f 0 for x x and f x, 0 0. Assumpton 1 s motvated by our conecture that fully unfar outsde opton s lkely to be gnored entrely by the player and fully far outsde opton s lkely to be most salent. Assumpton 2 says that the weght ncreases as the outsde opton becomes more equal and decreases otherwse. Furthermore, the outsde opton whch assgns everythng to me can be more pertnent to me as the one whch assgns everythng to the other player. Ths assumpton s consstent and could be ustfed by arguments akn to Fehr and Schmdt (1999) and Bolton and Ockenfels (2000). A smple example of such farness weghtng functon s 2 x 1 f x, 1 4 x. Notce that the outsde opton s most salent when x 2 and x x are equal and completely neutral when player gets nothng on the outsde. x 4

5 Our noton of farness weghtng s consstent wth the ntrgung results reported n the lterature, Dufwenberg and Gneezy s (2000) or Brandts et al. (2006). Take Dufwenberg and Gneezy as an example. In ther game they vary the outsde opton x of the frst mover to be 4, 7, 10, 13, and 16, whle keepng the outsde opton of the second mover to be 0. If the frst mover does not take the outsde opton, the second mover gets to splt a pe of 20; gvng y to the frst mover and keepng 20 - y. Because n all of ther treatments the outsde opton of the second mover s fully unfar (zero), then accordng to our farness weghtng conecture the percepton of t by the second mover should always be the same (0,0). Indeed, Dufwenberg and Gneezy do not fnd any correlaton between x and y and nether the y s to be statstcally sgnfcantly dfferent between treatments. But not all evdence from the lost wallet game supports farness weghtng. Charness, Haruvy, and Sonsno (2007) fnd a relatonshp between the sze of the outsde opton avalable to the frst mover and the decson of the second mover n an experment conducted over the nternet usng a wthn subects desgn and a strategy method. Due to ther choce of the desgn t remans unclear to what extent does the use of the strategy method play a role n determnng the results. We thnk that n ths partcular scenaro (and especally wthn subects) t can be prone to producng a monotonc relatonshp between the varables of nterest. Hence, we avod usng the strategy method and desgn our experment n a way that allows us to test whether NBS can shed some lght on subect s behavor. 2. The Experment Our experment conssts of two treatments mplemented n across-subect desgn. In both treatments the subects play the lost wallet game presented n Fgure 1. The frst mover chooses IN or OUT. If he chooses OUT, the game ends. The frst mover receves $10 ($5) and the second mover receves $0 ($5). If the frst mover chooses IN, the game contnues. The second mover then chooses how to splt $30 between the two of them n $1 ncrements. That s, the second mover chooses how much of $30 to gve to the frst mover, (y), and how much of t to keep, 30 y. The second mover s choce determnes the fnal payoffs. In the experment we keep the 5

6 total outsde opton pe constant at 10 n order to avod a possble confoundng effect that subects behave dfferently because there s a dfferent amount of money on the table. Fgure 1. The Lost Wallet Game Frst mover IN OUT 10 [5] 0 [5] Second mover y 0 [ y ] 30 [ 30 y ] The predcted behavor can vary between the two treatments for number of reasons that were already mentoned and we do not want to favor any of them. However, let us use the noton of psychologcal forward nducton to llustrate the possble effect of farness-weghtng n our experment. Psychologcal forward nducton appled to our game yelds very smple predctons. In the 10,0 treatment f the outsde opton was forgone by the frst mover ths should ndcate to the second mover that hs opponent expects at least 10 n the chosen subgame. If the second mover cares about the frst mover s expectatons, e.g., f he s gult-averse, then he should return at least 10. Thus, wthout farness-weghtng, the psychologcal forward nducton predcts that the frst mover s lkely to receve more n the 10,0 treatment than n the 5,5 treatment. On the other hand, wth farness-weghtng, the outsde opton s perceved dfferently. In the treatment 10,0 the outsde opton s perceved as (0,0) and n treatment 5,5 t s perceved as (5,5) by the second mover. Hence, f the percepton of the second mover matters n the way descrbed, then 6

7 we have truly vared the outsde opton between our treatments. The psychologcal forward nducton then predcts that the frst mover s lkely to receve more n the 5,5 than n the 10,0 treatment. 2.1 Procedures The sessons were conducted n October of 2006 n the SonderForschungsBerech 504 laboratory at the Unversty of Mannhem n Germany. A total of 22 subect pars partcpated n the 10,0 treatment and 21 subect pars n the 5,5 treatment. Most of the students had prevously partcpated n economcs experments, ncludng trust games. On average, a sesson lasted about 35 mnutes. Subects earned on average Euro plus n addton to a 4 Euro show up fee. Durng the experment all earnngs were calculated n expermental dollars. At the end of the experment the subects earnngs were converted to Euro at the rate of 1 expermental dollar = 0.5 Euro. All sessons were computerzed and run under sngle blnd protocol usng drect response elctaton method 1 The partcpants were randomly and anonymously matched nto pars that conssted of the frst mover and the second mover. The assgnment was done accordng to the followng process. Upon enterng the laboratory subects drew a ball from an urn. The number that was ndcated on the ball assgned ther seat for the experment. The computer workstatons were matched nto fxed pars to provde the maxmum possble dstance between frst and second movers wthn each par. Ths was unknown to the subects. Each subect was provded a hard copy of Englsh nstructons that were dentcal across subects. After the subects fnshed readng the nstructons they were asked to fll out a control questonnare to check for understandng. The expermenters verfed ther answers and prvately answered questons. Then the expermenters publcly provded the correct answers to the questonnare. 1 Ths was done n order to address our concerns wth the strategy method n the gven envronment, although the strategy method would yeld a hgher number of responses by the second movers. For comparson, Dufwenberg and Gneezy (2000) use only 13 subect pars n each of ther treatments. 7

8 2.2 Results Fgure 2 presents the summary of data for both treatments. Treatment 10,0 s dsplayed on the left and treatment 5,5 on the rght. Not surprsngly, twelve out of twenty two (55%) frst movers chose OUT when the outsde opton was 10 n comparson to seven out of twenty one (33%) when t was 5. However, ths dfference s statstcally not sgnfcant at the conventonal level (p = Fsher exact test 2-sded). Recall that the f the outsde opton s weghted by ts farness, the second mover, f called upon play, s lkely to mplement a splt wth a hgher y n the 5,5 than n the 10,0 treatment. In our data we observe that the second movers chose on average y = 10.8 and y = 8.1 n 10,0 and 5,5 treatments, respectvely. In order to assess the qualtatve dfference n the data, we test a hypothess that the choces of y are hgher n the unequal 10,0 than n the equal 5,5 treatment. However, the 1-sded two-sample Wlcoxon rank-sum test reports that ths dfference s not sgnfcant (p = 0.144). Consequently, the hypothess that choces of y are hgher n the 5,5 treatment than n the 10,0 one, as predcted by the relatve farness of the outsde optons, s reected at p = Hence, we conclude that the farness of the outsde opton dd not affect the subects behavor n our game. Fgure 2. Subects Behavor 8

9 3. Dscusson In ths paper we tred to address the queston whether the second mover gnores the forgone outsde opton by the frst mover as found n the prevous lterature because t gves everythng to the frst mover. We chose to derve predctons based on a functon whch weghts the relatve farness of outsde optons. Our data reect the conecture that t s the farness property whch could be responsble for ths effect. The result seems consstent wth Cox et al. (2007) who model recprocty based on what s the maxmal avalable payoff to the second mover followng the frst mover s acton. From that perspectve, the outsde opton s rrelevant, as we have observed n our experment. References Battgall, P. and M. Dufwenberg, Dynamc Psychologcal Games, Journal of Economc Theory, forthcomng. Battgall, P. and M. Dufwenberg, Gult n Games, Amercan Economc Revew, Papers & Proceedngs, 97, 2007, Bolton, G. E. and A. Ockenfels, "ERC: A Theory of Equty, Recprocty, and Competton," Amercan Economc Revew, vol. 90(1), 2000, Brandts, J., W. Güth, and A. Stehler, I Want YOU! An Experment Studyng Motvatonal Effects When Assgnng Dstrbutve Power, Labour Economcs 13, 2006, Brandts, J. and C. Solà, Reference Ponts and Negatve Recprocty n Smple Sequental Games, Games and Economc Behavor 36, 2001, Charness, G., E. Haruvy, and D. Sonsno, Socal Dstance and Recprocty: An Internet Experment, Journal of Economc Behavor and Organzaton, 63(1), 2007, Charness, G. and M. Rabn, Understandng Socal Preferences wth Smple Tests, Quarterly Journal of Economcs, 117(3), 2002, Cox, J. C. and C. A. Deck, On the Nature of Recprocal Motves, Economc Inqury, 2005, 43(3), Cox, J. C., D. Fredman, and S. Gerstad, "A Tractable Model of Recprocty and Farness," Games and Economc Behavor, 59, 2007,

10 Dufwenberg, M. and U. Gneezy, Measurng Belefs n an Expermental Lost Wallet Game, Games and Economc Behavor, 30, 2000, Dufwenberg, M. and G. Krchsteger, A Theory of Sequental Recprocty, Games and Economc Behavor, 47, 2004, Falk, A., E. Fehr, and U. Fschbacher, On the Nature of Far Behavor, Economc Inqury, 41(1), 2003, Falk, A. and U. Fshbacher, A Theory of Recprocty, Games and Economc Behavor 54, 2006, Fehr, E. Schmdt, K. M., A Theory of Farness, Competton, and Cooperaton, Quarterly Journal of Economcs 114, 1999,