Working Paper Loss aversion and rent-seeking: An experimental study

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1 econstor Der Open-Access-Publkatonsserver der ZBW Lebnz-Informatonszentrum Wrtschaft The Open Access Publcaton Server of the ZBW Lebnz Informaton Centre for Economcs Kong, Xaojng Workng Paper Loss averson and rent-seekng: An expermental study CeDEx dscusson paper seres, No Provded n Cooperaton wth: The Unversty of Nottngham, Centre for Decson Research and Expermental Economcs (CeDEx) Suggested Ctaton: Kong, Xaojng (2008) : Loss averson and rent-seekng: An expermental study, CeDEx dscusson paper seres, No Ths Verson s avalable at: Nutzungsbedngungen: De ZBW räumt Ihnen als Nutzern/Nutzer das unentgeltlche, räumlch unbeschränkte und zetlch auf de Dauer des Schutzrechts beschränkte enfache Recht en, das ausgewählte Werk m Rahmen der unter nachzulesenden vollständgen Nutzungsbedngungen zu vervelfältgen, mt denen de Nutzern/der Nutzer sch durch de erste Nutzung enverstanden erklärt. Terms of use: The ZBW grants you, the user, the non-exclusve rght to use the selected work free of charge, terrtorally unrestrcted and wthn the tme lmt of the term of the property rghts accordng to the terms specfed at By the frst use of the selected work the user agrees and declares to comply wth these terms of use. zbw Lebnz-Informatonszentrum Wrtschaft Lebnz Informaton Centre for Economcs

2 Centre for Decson Research and Expermental Economcs Dscusson Paper Seres ISSN CeDEx Dscusson Paper No Loss Averson and Rent-Seekng: An Expermental Study Xaojng Kong October 2008

3 The Centre for Decson Research and Expermental Economcs was founded n 2000, and s based n the School of Economcs at the Unversty of Nottngham. The focus for the Centre s research nto ndvdual and strategc decson-makng usng a combnaton of theoretcal and expermental methods. On the theory sde, members of the Centre nvestgate ndvdual choce under uncertanty, cooperatve and non-cooperatve game theory, as well as theores of psychology, bounded ratonalty and evolutonary game theory. Members of the Centre have appled expermental methods n the felds of Publc Economcs, Indvdual Choce under Rsk and Uncertanty, Strategc Interacton, and the performance of auctons, markets and other economc nsttutons. Much of the Centre's research nvolves collaboratve projects wth researchers from other departments n the UK and overseas. Please vst for more nformaton about the Centre or contact Karna Whtehead Centre for Decson Research and Expermental Economcs School of Economcs Unversty of Nottngham Unversty Park Nottngham NG7 2RD Tel: +44 (0) Fax: +44 (0) karna.whtehead@nottngham.ac.uk The full lst of CeDEx Dscusson Papers s avalable at

4 Loss Averson and Rent-Seekng: An Expermental Study* Abstract: We report an experment desgned to evaluate the mpact of loss averson on rent-seekng contests. We fnd, as theoretcally predcted, a negatve relatonshp between rent-seekng expendtures and loss averson. However, for any degree of loss averson, levels of rent-seekng expendture are hgher than predcted. Moreover, we fnd that the effect of loss averson becomes weaker wth repetton of the contest. * I am ndebted to my supervsors Martn Sefton, Klaus Abbnk, Bouwe Djkstra and Rchard Cornes for ther ncredble support and valuable comments; ther remarks nfluenced ths study consderably. In addton, I am especally grateful to Chrs Starmer for very useful suggestons on the expermental desgn. Thanks also to Png Zhang, Xanghua Zhang and Bn Xao for assstance n conductng the experments. Fundng of the experments by the Centre for Decson Makng and Expermental Research (CeDEx) of the Unversty of Nottngham s gratefully acknowledged. I wsh to thank Smon Gachter, Alex Possajennkov, Robn Cubtt and Danel Sedmann, as well as partcpants at the CREED-CeDEx Workshop, Nottngham, 2005, and the Economc Scence Assocaton Asa-Pacfc Regonal Meetng, Hong Kong, 2006, for helpful and encouragng comments. Any errors reman my own. 1

5 1. Introducton The term rent-reekng was ntally coned by Krueger (1974) to descrbe the contest of lobbyng to obtan a monopoly rent from the government. Snce then t has been appled to many economc and socal settngs n whch ndvduals expend resources or efforts n attempts to wn somethng of value. Standard examples of rent-seekng behavor nclude poltcal canddates competton for an offce, frms expendng R&D resources to secure a patent, and perodc contests among ctes and countres to host Olympc Games. Resources spent n rent-seekng are generally consdered a pure socal waste, because the resources are not used productvely. Therefore, an mportant queston rased n the theory of rent-seekng concerns the extent of rent dsspaton,.e. the amount of resources spent as a fracton of the prze. Most theoretcal accounts of rent-seekng study the nteracton of expected utlty maxmzers. Useful revews of ths lterature can be found n Ntzan (1994) and Hllman (2003, Chapter 6). There s, however, a growng body of evdence that many ndvduals systematcally devate from expected utlty maxmzaton. For example, there s consderable evdence of loss averson : startng from a gven level of ntal wealth, the aggravaton people experence n losses looms larger than the pleasure assocated wth gans of dentcal magntude (Kahneman and Tversky 1979). Recently Cornes and Hartley (2003) have shown theoretcally that loss averson reduces rent dsspaton. In ths paper we use expermental methods to ask whether loss averson n fact affects rent-seekng. The experment utlses the basc model for analyzng rent-seekng contests ntroduced by Tullock (1980). Ths model descrbes the rent-seekng process as a lottery, where rent seekers nvest resources competng for an exogenous ndvsble prze. Specfcally, we examne three-person contests where player wns the prze wth 3 probablty x / j = x 1 j, where x j denotes the expendture of player j. Ours s not the frst experment to study the Tullock rent-seekng model. Most of the earler studes have found observed dsspated rates to be hgher than theoretcally predcted. The frst experment to study the Tullock model was conducted by Mllner and Pratt (1989), who found dsspaton rates were sgnfcantly hgher than predcted. In a further experment (Mllner and Pratt 1991) they nvestgated the effect of rsk averson on 2

6 rent dsspaton. They found that more rsk-averse subjects spend less on rent-seekng. 1 Davs and Relly (1998) and Potters et al. (1998) also fnd over-dsspaton n ther experments. More recently, Schmdt et al. (2003) compare rent-seekng behavor across three dfferent mechansms. In ther mechansm correspondng to the Tullock model they observe lower levels of rent dsspaton than predcted. In ther experment, subjects play a one-shot game, the rent prze s set at $72, and each subject s only gven an endowment of $20; ths may account for lower rent-seekng expendtures than the theoretcal predctons. The only experment whch fnds dsspaton of rent consstent wth the theoretcal predcton s by Shogren and Bak (1991), who provde subjects wth a complete payoff matrx showng the expected payoff of all possble choces made by a subject and her opponent. Our experment s the frst (as far as we are aware) to examne the mpact of loss averson on rent-seekng. We frst elcted measures of each subjects loss averson, and then dvded our subjects nto more loss-averse and less loss-averse sub-samples. We then compared the rent-seekng behavor of the two sub-samples. We fnd, as predcted, that expendtures on rent-seekng are lower n the more loss-averse sub-sample. However, for any degree of loss averson, levels of rent-seekng expendture are hgher than predcted. Thus, although loss averson can reduce the extent of rent dsspaton n rent-seekng contests, we observe (as n prevous experments) over-dsspaton. Moreover, we also fnd that the dfference n rent-seekng expendtures between the two sub-samples dmnshes as subjects accumulate experence wth the contest. The remander of the paper s organzed as follows. In the next Secton we present Cornes and Hartley s (2003) extended rent-seekng model, ts equlbrum predcton and comparatve statc propertes. Secton 3 descrbes the expermental desgn and procedures. Secton 4 presents the expermental results. Secton 5 concludes. 2. The Model 2.1 The Value Functon and Loss Averson Loss averson s a central feature of Kahneman and Tversky s (1979) prospect theory, 1 They found that the rent dsspaton rate of the more rsk-averse subjects was consstent wth the Cournot-Nash rsk-neutral predcton, whle the less rsk-averse subjects spent more than rsk-neutral predctons. 3

7 n whch a value functon s defned over gans and losses relatve to some reference pont, rather than absolute levels of wealth. The specfc fndng known as loss averson s that the value functon s steeper n the doman of losses than n the doman of gans. In order to focus on the mplcaton of loss averson, we confne our attenton to a pecewse lnear value functon w v ( w) = λ w f f w 0, (*) w < 0 where w denotes a change n wealth, λ 0 denotes player s ndex of loss averson, and we take the reference pont to be player 's ntal wealth, W. 2 Player s strctly loss-averse f λ > 1, s loss-neutral fλ = 1 and s loss-seekng f λ < 1. The hgher sλ, the more loss-averse s player. 2.2 Rent-seekng wth Loss-averse Players Consder n ( n 2 ) players contestng an exogenous ndvsble prze R. Player has an ntal wealth level W and chooses to spend the level of resources x n an attempt to wn the prze. We assume that player s probablty of wnnng the prze s x / X = x /( x + X ), where X denotes the total resources spent by all the players, X n = j = 1 x j, and X s the sum of resources spent by all players except player. Ths s a smple form of Tullock s rent-seekng model (1980) n whch the odds of a player wnnng the prze s lnear n her expendture. Cornes and Hartley (2003) ncorporate loss averson nto ths model. Wthout loss of generalty, restrct x R, so that f player wns the prze she wll gan R x ; otherwse, she wll suffer a loss of x. Usng value functon (*), and assumng lnear probablty weghtng, player s payoff functon can be wrtten as whch can be rearranged as x x π ( x, X ) = ( R x ) + (1 ) λ ( x ), x + X x + X 2 Prospect theory also allows for curvature n the value functon n the loss and gan domans. The theory also allows for non-lnear probablty weghtng. In what follows, and agan n order to focus on pure loss averson, we wll assume a lnear probablty weghtng functon. 4

8 π x (.) = [ R + ( λ 1) x ] λ x + X x. If R λ X, then x x π (.) [ λ X + ( λ 1) x ] λ x = 0. x + X x + X 2 Snce choosng x = 0 gves a payoff of 0, the optmal choce when R λ X s x = 0. If R > λ X, then the frst order condton for maxmzng the payoff π s 3 [ λ ] [ λ ] ( ) 2 π ( x + X ) R+ 2( 1) x x R+ ( 1) x = λ = 0. x x + X After some rearrangement, the frst order condton can be wrtten as x 2x X + λ X RX = 0. Ths can be solved to gve the optmal x as a functon of X : x = X ) X + ( λ RX. Thus, player s best response functon s: X xˆ = 0 + (1 λ ) X 2 + RX f R > λ X f R λ X Fgure 1 shows the graph of best response functons wth dfferent ndces of loss averson. 4 It shows that gven a total amount of expendture by her rvals, the more loss-averse she s. --- Fgure 1 about here ---. X, player wll spend less Cornes and Hartley (2003) examne propertes of equlbra under the assumpton that all players have the same ndex of loss averson,.e. λ = λ for all. If players are not extremely loss-averse ( λ 2 ), 5 they show that there s a unque Nash equlbrum of the 3 2 The second order condton s 2 X [( λ 1) X R] π = < 0, whch s satsfed snce R > λ X. 2 3 x ( x + X ) 4 Strctly speakng, the best response s not defned when X = 0 subject to x > 0. Ths does not affect the exstence or propertes of equlbrum., snce n that case player would want to mnmze x, 5 When players are very senstve to loss ( λ > 2 ), although there s a unque symmetrc equlbrum, there may exst 5

9 rent-seekng contest, at whch the expendture of each player s R ( n 1) xˆ =. 2 2 ( λ 1)( n 1) + n Ths expresson shows a negatve relatonshp between equlbrum expendture ( xˆ ) and the ndex of loss averson ( λ ). Thus, an ncrease n players averson to loss decreases equlbrum expendture at both the ndvdual and the aggregate levels. Ths comparatve statc property of Cornes and Hartley s model s the bass for our expermental desgn, whch wll be descrbed n more detal n the next secton. 3. Expermental Desgn and Procedure The experment was conducted n May 2005 at the CeDEx laboratory at the Unversty of Nottngham. Subjects were recruted by e-mal from a unversty-wde pool of students to take part n a two-sesson experment. The sessons were conducted two days apart. In the frst sesson, we ran a pre-test to assess subjects ndvdual atttudes to loss and dvded them nto two categores, one relatvely more loss-averse than the other. In the second sesson, subjects classfed n the same loss category played rent-seekng contests wthn fxed three-person groups for 30 rounds Elctng Measures of Loss Averson Kahneman et al. (1990) appled a smple method to derve an estmate of subjects loss averson on average. They randomly assgned subjects to two condtons: sellers and buyers. Each seller was gven a coffee mug and was asked the mnmum offer she would accept n exchange for t (WTA - wllngness to accept). Buyers were gven nothng and asked the maxmum prce they would be wllng to pay for the mug (WTP - wllngness to addtonal asymmetrc equlbra. More dscusson can be found n Cornes and Hartley (2003). In our experment, only 2 out of 73 subjects had an estmated λ hgher than 2. 6 The nstructons for both sessons are ncluded as an appendx. Both sessons were computerzed usng the software package z-tree (Fschbacher, 1999). For techncal reasons the 30 rounds of rent-seekng games conssted of 3 sets of 10 rounds, wth two-mnute breaks at the end of rounds 10 and 20 rounds to reset software; durng the breaks subjects were not allowed to talk or leave ther seats. We examned our data for restart effects and faled to fnd any. 6

10 pay). In ther experment, the observed rato between the medan value of WTA among sellers and WTP among buyers was about 2. They used loss averson to explan ths dsparty and took the rato of medan WTA to WTP as a measure of loss averson. For our experment, we modfed the method used by Kahneman et al. (1990) n order to elct ndvdual-specfc measures of loss averson. In our frst sesson, subjects were requred to answer 120 bnary choce decson-makng questons. At the begnnng of the sesson, subjects receved nstructons that explaned the decson tasks and the mechansm used to determne ther earnngs. Each subject knew that one of the 120 decson questons, to be drawn randomly by computer at the end of the sesson, would be for real and the fnal payoff for ths sesson depended on her answer to ths randomly selected queston. The 120 questons were dvded nto two sets of 60 questons. Questons n the frst set were desgned to elct each subject s WTA valuatons on three dfferent goods: a box of chocolates, a notebook and a coffee mug that were normally sold at 2.50, 1.99 and 3.25 respectvely n the Students Unon Shop. 7 After nspectng samples of the three goods, subjects had to answer the frst set of questons. The questons were structured as Suppose you have Good A, would you lke to sell t for X?, where Good A was one of the three tems lsted above and the range of X was between 1.50 and 7.20, wth a varaton of Accordngly, we had 60 questons n the frst set, whch were programmed to dsplay on computer screen n a random order. A subject could see 10 questons per screen and she had to complete all the questons shown on the screen before movng on to the next screen. A consstent subject would refuse to sell a good at all prces below her WTA and would agree to sell at any prce hgher than her WTA. For example, f a subject gves negatve answers to questons Suppose you have the mug, would you lke to sell t for X? untl the amount of X exceeds 4.50 and afterwards her responses are always postve, then we estmate her WTA for the mug to be When all our subjects had gven ther answers to the frst 60 questons, we calculated each one s WTA valuatons for the three goods. At the same tme a questonnare was handed out to each subject to fll n. 8 7 The reason we chose these three tems n our experment s that we expected most of our subjects to be famlar wth them, so that they could easly place ther own valuaton on them. Subjects may also have been aware of the market prce of these goods; Bateman et al. (1997) shows that whether or not subjects know the market prce of a good does not affect the psychologcal mpact of loss averson for t. 8 The questonnare ncluded questons about students famlarty wth the goods. It was manly ntended as a fller task, to gve subjects somethng to do whle the expermenter calculated each subject s WTA for the three goods. 7

11 About ten mnutes later, we gave a second set of 60 questons, whch were amed to derve subjects WTP for the same goods. Questons n ths set had the followng form: If you have M n cash, would you lke to pay Y to buy Good B? Good B was one of the three goods that appeared n the frst set of questons and Y ranged from 1.50 to Gven a subject s answers to the second set of questons, we used the same method as before to derve her WTP valuatons for the three goods. A novel aspect of our expermental desgn s that the amount appearng n the second set of questons, M, was the estmate of each subject s WTA for Good A. For nstance, from the frst set of questons, f a subject s WTA valuatons were judged as 6.30, 5.40 and 4.80 for the mug, chocolates and notebook respectvely, then the questons created to her n the second set would be: If you have 6.30 (/ 5.40/ 4.80), would you lke to pay Y to buy the mug (/the box of chocolates/the note book)? Therefore, dfferent subjects may have dfferent settngs of M for the same good. Ths desgn allows us to control the effects of ncome and the elastcty of substtuton whch Hanemann (1991) suggested may account for some of the dvergences between WTA and WTP. In the frst set of questons, a subject starts from the reference pont R (see Fgure 2), where she owns Good A wthout any money. If M s the mnmum offer she would accept n exchange for Good A, then pont R and M produce the same utlty to her from the reference pont R, and the estmaton of her WTA for Good A s M. In the second set of questons, we set subject s reference pont at pont M, where she doesn t own Good A but s endowed wth M, the same amount as her WTA for Good A. Startng from the reference pont M, f Y s the maxmum prce she s wllng to pay for Good A, then pont M and P produce the same utlty to her, Y s our estmaton of her WTP. The dfference between her WTA ( M) and WTP ( Y) can be easly explaned by loss averson: snce Good A s valued as a loss from the ntal reference pont R but a gan from the reference pont M, the dfference between M and Y reveals that the dsutlty of gvng up Good A s greater then the utlty of recevng t. Loss averson s ncompatble wth the neoclasscal theory of consumer choce, as shown by the ndfference curves RM and MP that ntersect at M. However, n the second set of questons, f the subject s endowment s not exactly equal to her WTA ( M), the dsparty between WTA and WTP could be consstent wth neoclasscal theory. For example, f n the second set of questons, the subject s endowed 8

12 wth M, because the ndfference curves RM and QM do not ntersect, the shape of the ndfference curve, rather than loss averson, could explan the dfference between M and Y. --- Fgure 2 about here --- Based on the estmates of subjects WTA and WTP valuatons, we calculated the average WTA/WTP rato over the three goods for each subject. We used ths rato as an estmate of a subject s ndex of loss averson, and usng these estmates we dvded our subjects nto two categores, one relatvely more loss-averse than the other. Seventy-three subjects partcpated n the frst sesson, whch lasted about 40 mnutes. Of these, 13 seemed just to gve ther answers casually wthout any serous consderaton. For example, for questons Suppose you have a mug, would you lke to sell t for 1.50/ 2.70/ 4.20/ 5.40/ 6.90?, a subject gave her answers as No/Yes/No/Yes/No. It s dffcult for us to judge her WTA or her ndex of loss averson. For that reason, we excluded these nconsstent subjects from our second sesson. The remanng 60 subjects gave consstent responses and took part n our second sesson. For the 60 consstent subjects, the medan ndex of loss averson (WTA/WTP) was 1.14 and only 3 subjects had ther WTA/WTP ratos less than 1. The thrty subjects wth ther WTA/WTP ratos hgher than 1.14 were classfed as more loss-averse. The other thrty subjects wth WTA/WTP ratos lower than 1.14 were classfed as beng less loss-averse. On average, both categores of subjects who took part n the second sesson of the experment were loss-averse, as the mean WTA/WTP ratos were 1.52 and 1.03 for the more and less loss-averse categores respectvely. 3.2 The Rent-Seekng Sesson A total of 30 less loss-averse and 30 more loss-averse subjects took part n the second sesson, where they played 30 rounds of rent-seekng game wthn fxed three-player groups. Ths part of the experment conssted of four sub-sessons wth 15 subjects each and subjects n the same sub-sesson were taken from the same loss-averse category. Altogether we had 10 groups wth more loss-averse subjects and 10 groups wth less lossaverse subjects. In ths sesson, all expendtures, przes and earnngs n the game were stated n terms of taler, an expermental currency. At the end of the experment, the total amount of talers 9

13 subjects earned throughout the 30 rounds was converted to Brtsh pounds at an exchange rate of 1000 talers to 1 and pad to subjects anonymously n cash. Each sub-sesson lasted between 40 and 55 mnutes and subject earnngs ranged from 7.53 to Average earnngs were 9.30 for subjects n the more loss-averse category and 8.92 for subjects n the less loss-averse category; the former was sgnfcantly hgher than the latter (Wlcoxon Rank Sum test, one-sded p-value = 0.029). In each sub-sesson, before the rent-seekng game started, wrtten nstructons were handed out and read aloud to subjects. These nstructons provded comprehensve descrptons of the expermental procedure and the payoff structure. At the begnnng of the frst round, each subject was randomly assgned to a three-player group whch remaned fxed throughout the sesson and knew that two of the other fourteen people n the room were n her group, but had no dea whch two. In each round, subjects were gven an ntal endowment of 300 talers, whch they could use to buy lottery tckets costng one taler apece to compete for a prze of 200 talers wth the other two players n ther groups. Subjects were nformed how ther wnnng probabltes and round payoffs were calculated and they were also aware that when all group compettors had made decsons on how many tckets to buy, one tcket wthn a group would be randomly drawn by the computer to decde the wnner. Feedback was dsplayed on subjects screens at the end of each round and ncluded nformaton about the wnner of the group, the number of tckets purchased and the round payoff of each group member. Subjects were also kept updated on ther accumulated payoffs before every new round began. Wth ths desgn, the comparson of expendtures between our two sub-samples allows us to test our prmary hypothess that rent-seekng expendtures wll be hgher n the less loss-averse sub-sample. In addton, the repetton of the rent-seekng task n our desgn enables us to examne the role played by learnng n rent-seekng contests. The ntal behavor of subjects may plausbly depend on ther expectatons about others behavor. Whereas n equlbrum these expectatons are assumed to be correct, n our experment we do not expect ths to be necessarly the case. Thus the equlbrum expressons n Secton 2 may predct subject behavor more closely n later rounds, after subjects have had a chance to learn about the behavor of others. 10

14 4. Expermental Results 4.1 Early Round Behavor: Rounds 1-10 In the very frst round we observe a clear relatonshp between rent-seekng expendtures and loss averson. Fgure 3 presents a scatter-plot of ndvdual expendtures n round one aganst the measure of loss averson taken from the elctaton sesson. Also shown s an OLS regresson lne where the coeffcent on loss averson s negatve and sgnfcant (t = 2.34, one-sded p-value = 0.012). Non-parametrc analyss of the data yelds the same concluson: the correlaton between ndvdual expendtures n round one and ndvdual ndces of loss averson s negatve and sgnfcant (Spearman Rank-Order Correlaton Coeffcent = 0.28, one-sded p-value = 0.016) Fgure 3 about here --- Ths pattern holds beyond the frst round. Because ndvduals nteract n fxed groups wth no nformaton passng between groups, we base nferences on group-level data. For each group we measure loss averson as the average of each group member s ndex of loss averson, and compare ths wth average group expendtures. Fgure 4 presents a scatter-plot of average group expendture over the frst ten rounds aganst the measure of loss averson (thus, each pont n the scatter-plot corresponds to a three-person group). Also shown s an OLS regresson lne, whch agan dsplays a negatve and sgnfcant coeffcent on loss averson (t = 2.53, one-sded p-value = 0.011). Agan, non-parametrc test supports ths concluson: the average group expendture over the frst ten rounds s negatvely and sgnfcantly correlated wth the measure of loss averson (Spearman Rank-Order Correlaton Coeffcent = 0.43, one-sded p-value = 0.029). --- Fgure 4 about here --- Gven these data, t should not be surprsng that when we compare the more loss-averse and less loss-averse sub-samples the comparatve statc predctons of Secton 2 are borne out. Table 1(a) shows the average expendture of groups n the frst ten rounds. Expendtures by less loss-averse groups are 35% hgher than expendtures by more loss-averse groups. The dfference s sgnfcant, based on a Wlcoxon Rank Sum test (one-sded p-value = 0.021), and strongly confrms the hypothess that more loss-averse 9 One-sded tests are approprate n our context as the theoretcal consderatons of Secton 2 suggest a drectonal alternatve to the null hypothess of no relatonshp between expendture and loss averson. 11

15 expendtures wll be closer to equlbrum n the second ten rounds. Smlarly we test whether group expendtures n the last ten rounds are closer to equlbrum than group expendtures n the second ten rounds. Note that n the frst 10 rounds, 9 out of 10 less loss-averse groups nvested more than the amount of the prze (200 talers) n rent-seekng (see Table 1(a)). Realzng ther group expendtures were too hgh, even hgher than the prze tself, all of these groups learned ther lessons fast and lowered ther expendtures n rounds As a result there s a sgnfcant tendency for group expendtures by less loss-averse groups to move closer to the loss-neutral predcton between the frst and second thrds of the sesson (Wlcoxon Sgned-Rank test, one-sded p-value = 0.005). However, we observe no such learnng effect after the second 10 rounds (Wlcoxon Sgned-Rank test, one-sded p-value = 0.930). Ths s despte the fact that n the second 10 rounds average group expendtures are talers per group per round, stll hgher than loss-neutral equlbrum (though somewhat less than the prze). For more loss-averse groups, no such learnng effect was found throughout the whole sesson (Wlcoxon Sgned-Rank test, one-sded p-values = and after the frst and second 10 rounds respectvely). These tests suggest that subjects reduce ther spendng when group expendture exceeds the amount of the prze, but they fal to adjust expendtures further, even though ths leaves expendtures stll hgher than predcted. Ths suggeston s supported by Fgure 8 whch depcts each ndvdual s average expendture over the three sets of 10 rounds, wth data from the less and more loss-averse sub-samples presented n Panels (a) and (b). Also shown are average best response functons (based on ndces of loss aversonλ = and 1.52, each correspondng to the average WTA/WTP rato for the relevant sub-samples), plotted as sold lnes. The Fgure also shows dashed lnes along whch group expendture s exactly equal to the prze; from the dashed lne, group expendture ncreases northeasterly and decreases southwesterly. Comparng the frst ten rounds wth the second ten t s clear that many ndvduals fnd themselves n groups where expendtures exceed the prze n the frst ten rounds, and then learn to reduce expendtures n the second ten rounds. However, a comparson of the thrd ten rounds wth the second ten shows that ths process does not converge to the equlbrum. Nether more nor less loss-averse groups learned to decrease ther expendture to the equlbrum predcted level. 14

16 --- Fgure 8 about here --- The analyss above s supported by further analyss usng ndvdual-level data. We examned how subjects adjusted ther expendtures from round to round. We frst examne whether subjects adjust ther expendture n the drecton of the best response. In our rentseekng sesson, subjects receved feedback at the end of each round about the number of tckets purchased by each group member and the earnngs of each group member. In prncple, subjects could have evaluated what decson would have maxmzed ther expected earnngs, takng as gven other subjects decsons. For example, f a subject has an ndex of loss averson of 1.56, and the total expendture by her rvals n round t s 100 talers, her best response functon suggests her optmal expendture to be 20 talers. Suppose her actual expendture n round t s 55 talers, then f she decreases her expendture n round t+1, she moves n the drecton of what her own best-response suggested; otherwse, she does not adjust her expendture n the drecton of her best response. Assumng subjects evaluate outcomes n ths way, then out of 29 rounds, the average number of expendture adjustments made by subjects n the best-response suggested drecton should be sgnfcantly hgher than 14.5, the number of adjustments n ths drecton that would be expected when adjustments were purely random. However, our results show that the average number of expendture adjustments n the predcted drecton s 14.5 and 11.9 for less and more loss-averse subjects respectvely. Therefore, subjects do not have a systematc tendency to move n the drecton of best responses to opponents prevous round choces. There are of course other ways n whch subjects could evaluate outcomes. For example, t seems obvous that f group expendtures exceed the prze then the group as a whole s losng money and should, from a group perspectve, decrease expendtures. In fact, even from an ndvdual perspectve a subject earns more f she reduces expendtures n ths case. 10 On the other hand, f group expendtures are below the value of the prze, t may not be so obvous to a subject why she should reduce expendtures. Indeed, suppose ndvdual expendtures do not exceed the prze (.e. x R for all ). Then the subject who 10 Ths s because the margnal earnngs from an addtonal unt of expendture s 2 π / x = X R / X 1. Ths s clearly less than 2 XR / X 1 = R/ X 1. In turn ths expresson s negatve f X > R. 15

17 wns the prze wll always earn the most money. The wnner of the prze s most lkely to be the subject who spent the most. Thus f subjects mtate the choces of the most successful player there wll be a tendency to ncrease expendtures. More formally, an mtate the best dynamc converges to full dsspaton n the long-run. 11 In order to examne how group expendtures adjusted relatve to the full dsspaton level, we tested formally whether there s a systematc tendency for groups to reduce ther expendture when ther total expendture s hgher than the prze, and ncrease t when ther total expendture s lower than the prze. Out of 29 rounds, the average number of the changes n group expendture n the drecton towards 200 talers s 19.5 and 17.3 for less and more loss-averse subjects respectvely; both of them are sgnfcantly hgher than the 14.5, the number of adjustments n ths drecton that would be expected when adjustments were purely random (Wlcoxon Sgned-Rank test, one-sded p-values = and for less and more loss-averse groups respectvely). Thus, dynamc adjustments of rent-seekng expendtures appear to move groups n the drecton of full dsspaton, rather than n the drecton of the Nash equlbrum. 5. Concluson The results of our experment show a clear negatve relatonshp between loss-averson and ntal rent-seekng expendtures. In the early rounds of the rent-seekng experment groups composed of more loss-averse subjects spend sgnfcantly less than groups composed of less loss-averse subjects. Ths confrms one of the suggestons from Cornes and Hartley s (2003) model: the exstence of loss averson can reduce rent dsspaton n rent-seekng contests. However, we also observed hgher levels of rent-seekng expendture than predcted for both more and less loss-averse sub-samples. Thus, although loss averson can reduce the extent of rent dsspaton n rent-seekng contests, we stll observe over-dsspaton. Moreover, the effect weakens wth repetton. The dfference between the expendtures of our two sub-samples s only sgnfcant for the frst 10 rounds; t s not sgnfcant for the later rounds. Further analyss of adjustments n rent-seekng expendtures showed some strong 11 Evolutonary game theory also suggests convergence toward full dsspaton. For example, n ths rent-seekng game Nash equlbrum strateges are not evolutonary stable, and the unque evolutonary stable strategy s for a player to spend one n th of the prze, leadng to full dsspaton by the n-member group (see Hehenkamp, Lennger and Possajennkov, 2004). 16

18 --- Fgure 8 about here --- The analyss above s supported by further analyss usng ndvdual-level data. We examned how subjects adjusted ther expendtures from round to round. We frst examne whether subjects adjust ther expendture n the drecton of the best response. In our rentseekng sesson, subjects receved feedback at the end of each round about the number of tckets purchased by each group member and the earnngs of each group member. In prncple, subjects could have evaluated what decson would have maxmzed ther expected earnngs, takng as gven other subjects decsons. For example, f a subject has an ndex of loss averson of 1.56, and the total expendture by her rvals n round t s 100 talers, her best response functon suggests her optmal expendture to be 20 talers. Suppose her actual expendture n round t s 55 talers, then f she decreases her expendture n round t+1, she moves n the drecton of what her own best-response suggested; otherwse, she does not adjust her expendture n the drecton of her best response. Assumng subjects evaluate outcomes n ths way, then out of 29 rounds, the average number of expendture adjustments made by subjects n the best-response suggested drecton should be sgnfcantly hgher than 14.5, the number of adjustments n ths drecton that would be expected when adjustments were purely random. However, our results show that the average number of expendture adjustments n the predcted drecton s 14.5 and 11.9 for less and more loss-averse subjects respectvely. Therefore, subjects do not have a systematc tendency to move n the drecton of best responses to opponents prevous round choces. There are of course other ways n whch subjects could evaluate outcomes. For example, t seems obvous that f group expendtures exceed the prze then the group as a whole s losng money and should, from a group perspectve, decrease expendtures. In fact, even from an ndvdual perspectve a subject earns more f she reduces expendtures n ths case. 10 On the other hand, f group expendtures are below the value of the prze, t may not be so obvous to a subject why she should reduce expendtures. Indeed, suppose ndvdual expendtures do not exceed the prze (.e. x R for all ). Then the subject who 10 Ths s because the margnal earnngs from an addtonal unt of expendture s 2 π / x = X R/ X 1. Ths s clearly less than 2 XR / X 1 = R / X 1. In turn ths expresson s negatve f X > R. 15

19 wns the prze wll always earn the most money. The wnner of the prze s most lkely to be the subject who spent the most. Thus f subjects mtate the choces of the most successful player there wll be a tendency to ncrease expendtures. More formally, an mtate the best dynamc converges to full dsspaton n the long-run. 11 In order to examne how group expendtures adjusted relatve to the full dsspaton level, we tested formally whether there s a systematc tendency for groups to reduce ther expendture when ther total expendture s hgher than the prze, and ncrease t when ther total expendture s lower than the prze. Out of 29 rounds, the average number of the changes n group expendture n the drecton towards 200 talers s 19.5 and 17.3 for less and more loss-averse subjects respectvely; both of them are sgnfcantly hgher than the 14.5, the number of adjustments n ths drecton that would be expected when adjustments were purely random (Wlcoxon Sgned-Rank test, one-sded p-values = and for less and more loss-averse groups respectvely). Thus, dynamc adjustments of rent-seekng expendtures appear to move groups n the drecton of full dsspaton, rather than n the drecton of the Nash equlbrum. 5. Concluson The results of our experment show a clear negatve relatonshp between loss-averson and ntal rent-seekng expendtures. In the early rounds of the rent-seekng experment groups composed of more loss-averse subjects spend sgnfcantly less than groups composed of less loss-averse subjects. Ths confrms one of the suggestons from Cornes and Hartley s (2003) model: the exstence of loss averson can reduce rent dsspaton n rent-seekng contests. However, we also observed hgher levels of rent-seekng expendture than predcted for both more and less loss-averse sub-samples. Thus, although loss averson can reduce the extent of rent dsspaton n rent-seekng contests, we stll observe over-dsspaton. Moreover, the effect weakens wth repetton. The dfference between the expendtures of our two sub-samples s only sgnfcant for the frst 10 rounds; t s not sgnfcant for the later rounds. Further analyss of adjustments n rent-seekng expendtures showed some strong 11 Evolutonary game theory also suggests convergence toward full dsspaton. For example, n ths rent-seekng game Nash equlbrum strateges are not evolutonary stable, and the unque evolutonary stable strategy s for a player to spend one n th of the prze, leadng to full dsspaton by the n-member group (see Hehenkamp, Lennger and Possajennkov, 2004). 16

20 smlartes between the adjustment patterns of the two sub-samples. Subjects n both sub-samples react to stuatons of over-dsspaton by reducng expendture. However, they do not reduce expendture all the way to the Nash equlbrum. Once the reducton s suffcent to help them escape group losses, they show no systematc tendency to further reduce expendtures. Rather, groups appear to move systematcally n the drecton of full dsspaton. The convergence n behavor of less and more loss-averse groups reflects ths pattern. In early rounds t was the less loss-averse groups that tended to spend more on rent-seekng than the value of the prze. These groups learned to reduce ther expendtures n later rounds, and ths brought ther expendtures n lne wth the more loss-averse groups. One reason why the effect of loss averson on rent-seekng behavor weakens over tme may be that atttudes to loss averson may change over tme. One possblty s that the degree of loss averson may change across rounds as subjects accumulate earnngs n the experment. Note that the more loss averse groups spend less on rent seekng n early rounds, and so we would expect that these groups to be wealther (relatve to the less loss averse groups) n later rounds. If wealther people are less loss averse, we would expect the dfferences n the atttudes toward loss averson between the two sub-samples to weaken. However, the only evdence of whch we are aware lnkng loss averson to wealth s a study by Johnson et al. (2006), who fnd that wealther people are more senstve to losses. Smlarly Barkan and Busemeyer (1999) fnd that subjects rsk preferences tend to swtch towards rsk averson after experencng a gan, and towards rsk seekng after experencng a loss. 12 A smlar pattern n our data (.e. less loss averse after experencng a loss) would amplfy, not erode, the dfference between sub-samples. More fundamentally, loss averson tself may be a transent phenomenon, only dsplayed by nexperenced subjects. Indeed, Lst (2003) suggests market experence can elmnate the WTA/WTP dsparty, and thus, loss averson s lmted to nexperenced subjects. Snce repetton of our rent-seekng game allows subjects to gan experence, t may be that repetton makes both groups effectvely loss-neutral n later rounds, and ths elmnates the orgnal dstncton between our two sub-samples. 12 A smlar argument that losses lead to more aggressve behavor n has been made n the context of real-world contests. In an emprcal study of twenteth century battles, Bauer and Rotte (1997) suggest that the experence of losses contrbutes postvely to the preparedness to contnue fghtng, up to a pont where casualtes clearly outwegh any drect utlty drawn from ordnary expected-utlty theory. 17

21 We fnd t ntrgung that even among subjects n our more loss-averse category, rent-seekng expendtures substantally exceed equlbrum predctons, and that ths substantal level of over-dsspaton perssts nto later rounds. Ths over-dsspaton s consstent wth other laboratory rent-seekng experments. Ths appears to be a form of anomalous behavor that s not elmnated by experence. Our experment was not desgned to nvestgate the reasons for such over-dsspaton, and we leave ths topc open for future research. 18

22 Group Table 1. Group expendture per round and dsspaton rate More Loss-averse Groups Rent-seekng Expendture (taler) (a) Round 1-10 Rent Dsspaton Rate Less Loss-averse Groups Rent-seekng Expendture (taler) Rent Dsspaton Rate Average (s.e.) (70.6) 0.89 (0.35) (47.3) (0.24) (b) Round Group More Loss-averse Groups Less Loss-averse Groups Rent-seekng Expendture (taler) Rent Dsspaton Rate Rent-seekng Expendture (taler) Rent Dsspaton Rate Average (s.e.) (69.3) 0.76 (0.35) (41.8) 0.90 (0.21) (c) Round Group More Loss-averse Groups Less Loss-averse Groups Rent-seekng Expendture Rent Dsspaton Rate Rent-seekng Expendture Rent Dsspaton Rate (taler) (taler) (63.5) (0.32) (35.1) (0.18) Average (s.e.) 19

23 Fgure 1. Best response functons wth dfferent ndces of loss averson ( λ 1 λ 2 < λ 3 < λ 4 < ) x 0 λ = λ 4 R λ = λ 3 R λ = λ 2 λ = λ4 λ3 λ2 1 λ 1 R R λ X 20

24 Fgure 2. Indfference curves and the dvergences between WTA and WTP Good A (unt) 1 R P Q 0 M M Y (WTP) Money ( ) Y (WTP ) M (WTA) M 21

25 Fgure 3. Indvdual expendtures n round one and ndces of loss averson x = λ (27.49) (20.42) R 2 =

26 Fgure 4. Group expendtures n rounds 1-10 and ndces of loss averson X = λ 2 (54.90) (41.31) R =

27 Fgure 5. Average group expendture n rounds

28 Fgure 6. Group expendtures n rounds 1-30 and ndces of loss averson X = λ (44.04) (33.14) R 2 =

29 Fgure 7. Average group expendtures n rounds

30 Fgure 8. Average Indvdual Expendture over three sets of 10 rounds (Round 1-10, Round11-20, Round 21-30) (a) Less Loss-Averse Subjects (b) More Loss-Averse Subjects x. Round Round 1-10 x x + X = 200 x + X = 200 X X x. Round Round x x X = 200 x X = X X x. Round Round x x X = 200 x X = X X X -Average total expendture by the other two group member of each 10 rounds x - Average ndvdual expendture of each 10 rounds 27

31 Appendx. Expermental Instructons General Instructons Thank you for comng to our experment. Ths experment conssts of 2 sessons. Today we are gong to run the frst sesson and the second one wll be run on ths Thursday (12 th of May). We ll wrte an emal to nform you the precse tme to come for the second sesson by 2pm ths Wednesday. The purpose of ths experment s to study how people make decsons n a partcular stuaton. Durng the experment t s not permtted to talk or communcate wth other partcpants. If you have any queston, please rase your hand and one of us wll come to your table to answer t. Durng the sessons you wll earn money and maybe some good as well (such as chocolates, notebook etc). At the end of the frst sesson you wll receve a statement sgned n acknowledgement of your earnngs; And at the end of the second sesson, the total amount you have earned from both two sessons wll be pad to you together. Payments are confdental, we wll not nform any other partcpant of the amount you have earned. Please keep the statement sgned n acknowledgement of your earnngs from the frst sesson safely and brng t wth you when you come to the second sesson ths Thursday (12 th of May). And please make sure that you would come and partcpate the second sesson of ths experment at the tme you nformed. Your absence from the second sesson could result n our experments breakng down, therefore you wll be unqualfed to clam what you have earned from the frst sesson. Thanks for your partcpaton. Instructons (for Sesson A) Ths sesson conssts of 120 bnary choce decson makng problems for you to answer. The sesson s dvded nto 2 parts: After every partcpant has completed the frst 60 questons, there s a questonnare for you to fll n; then partcpants begn to answer the other 60 questons. There are two types of questons n the sesson: Questons from 01 to 60 are lke: Suppose you have Good A, would you lke to sell t for X pounds? Questons from 61 to 120 are lke: If you have M pounds, would you lke to pay Y pounds to buy Good B? (Yes or No) (Yes or No) 28

32 At the end of ths sesson, the computer wll randomly draw one queston among all the 120 questons n the survey. Your fnal payoff for ths sesson depends on the answer you have made to ths randomly selected queston. If the randomly selected queston s one out of queston 01-60, Good A wll be handed to you frst. Then, f the answer you have gven s yes, we would buy (take) Good A from you and pay you X pounds as your fnal payoff for ths sesson; f the answer you have gven s no, you would keep Good A as your fnal payoff for ths sesson. If the randomly selected queston s one out of queston , you wll be gven M pounds as your credt frst. Then, f the answer you have gven s yes, we would sell (gve) Good B to you at a prce of Y pounds and your fnal payoff for ths sesson s: M pounds- Y pounds +Good B; f the answer you have gven s no, you would keep that M pounds as your fnal payoff for ths sesson. Durng the sesson, you are not allowed to talk or communcate. If you have any queston, please rase your hand and one of us wll come to your desk to answer t. Instructons (for Second Sesson) Thank you for comng to the second sesson of our experment. The purpose of ths experment s to study how people make decsons n a partcular stuaton. Durng the experment t s not permtted to talk or communcate wth other partcpants. If you have any queston, please rase your hand and one of us wll come to your table to answer t. Payment Durng the sesson you wll earn money, at the end of the sesson, the total amount you have earned wll be pad to you by cash. The unt of payoff shown n the nstructons and the computer screens are n talers, whch s the expermental currency used n ths sesson. At the end of the sesson your total payoff wll be converted nto sterlng at an exchange rate of 1 pound for each 1000 talers. Payments are confdental; we wll not nform any other partcpant of the amount you have earned. Ths sesson conssts of 30 rounds. At the begnnng of the frst round, you wll be randomly assgned to a group consstng of you and two other partcpants and your group members wll be the same durng the sesson. Rules of the decson stuaton n each round: In each round, you are competng for a prze of 200 talers wth the other two players n your group by purchasng lottery tckets. One of the three players n your group wll wn the prze and the probablty that you wn the prze depends on your own decson and the decsons made by the other two players n your group. 29

33 We wll begn every round by gvng you 300 talers as an ntal endowment, whch you can use to buy the lottery tckets. Each tcket costs you 1 taler, so you wll be able to buy up to 300 tckets every round. Each player wll separately make a decson on the number of lottery tckets he/she wsh to buy. When the decson has been made, please enter the number nto the computer. Your probablty of wnnng the prze depends on the number of tckets you buy and the number of tckets purchased by the other two players n your group. More precsely, the probablty that you wn the prze equals the rato of the number of tckets you buy and the total number of the tckets bought by all the 3 players n your group: Number of tckets you buy Probablt y of you wnnng the prze = Total number of tckets bought by your group If none of the players buys a tcket, each player wll have an equal chance (1/3) of wnnng the prze. After every player has made hs/her decson, the computer wll randomly draw one tcket among all the purchased tckets to decde who the wnner s. If you are the wnner, your round payoff wll be: Payoff = 300 (ntal endowment) the money you spent to buy lottery tckets (the prze of the lottery) If you are not the wnner, your round payoff wll be: Payoff = 300 (ntal endowment) the money you spent to buy lottery tckets At the end of each round you wll be nformed about the wnner of the lottery and the round payoff of yourself and your compettors. In addton, you wll also be able to see the result of prevous round and your updated total payoff. Payment: The payoffs shown n both the nstructons and the computer screens are n talers, whch s the expermental currency used n ths sesson. At the end of the sesson your total payoff wll be converted nto sterlng at the exchange rate of 1 pound for each 1000 talers. 30