Investigating Motives behind Punishment and Sacrifice:A Within-Subject Analysis∗
Luke Garrod†
August2009
Abstract
We analy an experiment that obrves each subject’s behaviour for both roles in the ultimatum and dictator game,and two modified ultimatum games where in the
event of a decline the propor and responder receive a-and(1-)-share of their
propod payoffs,respectively,where in our games=1(impunity game)and=0
(guarantor game).It is shown that inequality aversion or lf-interest cannot describe
the behaviour of over60%of subjects across a number of roles given reasonable
levels of error,becau many subjects sacrifice material payoffs without a pecuniary
punishment motive and some punish when the proposal is not unfavourable to them.
The within-subject analysis suggests that many of the former may be motivated by
a willingness to avoid‘unfair’bargains whereas a proportion of the latter may be
motivated by spite.
Keywords:ultimatum bargaining,inequality aversion,other-regarding preferences
JEL:C72,C91
1Introduction
In laboratory experiments,many subjects are willing to be‘nice’to people,especially if they are‘nice’to them,and are willing to be‘not nice’to people if they are‘not nice’to them.This type of reciprocal behaviour is evident in many experimental games but none more so than the ultimatum game(e Gth et al,1982)where responders are willing to decline low offers to eliminate a propor’s material payoffat the expen of their own; and in the dictator game where propors are willing to share some of a monetary surplus between themlves and another subject(e Forsythe et al,1994).1Such behaviour cannot
∗I am grateful to Robin Cubitt and Daniel Zizzo for extensive suggestions,and Graham Loomes,Peter Moffatt,Hans-Theo Normann,Anders Pouln,Martin Sefton,Robert Sugden,participants of the minar at the Royal Economic Society Annual Conference2006and anonymous referees for helpful comments. Thanks go to Ian Bateman and Katy Appleton for their help organising the Zuckerman Institute for Con-nective Environmental Rearch(ZICER)laboratory.The support of the Economic and Social Rearch Council(UK)is gratefully acknowledged.
†Post Doctoral Fellow,ESRC Centre for Competition Policy,University of East Anglia,email: l.garrod@uea.ac.uk
1In the ultimatum game,a propor offers a split of a monetary surplus to a responder,which can be accepted or declined.If accepted,players receive their propod shares;if declined,both receive nothing. In the dictator game,the propor’s division is implemented.For reviews of the不顾一切
ultimatum game literature (e Thaler1988;Camerer and Thaler,1995;Roth,1995;and Camerer,2003)
be explained by the standard economic assumption that people behave as if they are rationally lf-interested.2
Over the last decade or so,there have been veral attempts to explain this behaviour by relaxing the assumptions of lf-interest and integrating other-regarding preferences in an agent’s utility function.3Such theories assume that subjects receive utility from their material payoff,but they may also have preferences over the material payoffs of others in their reference group(e Fehr and Schmidt,1999;Bolton and Ockenfels,2000;Charness and Rabin,2002;and Cox et al,2007),their utility may be dependent on the fairness of others’behaviour(e Rabin,1993;and Dufwenberg and Kirchsteiger,2004;and Falk and Fischbacher,2006),or they may care whether others are intrinsically‘fair’or‘unfair’types (e Levine,1998).
In general,two of the main assumptions behind many of the theories are that agents sacrifice material payoffs to punish an opponent by eliminating some of his material payoff, and that this type of punishment is instigated when an opponent’s behaviour is‘unfair’or the distribution of payoffs is too unfavourable.To the contrary,evidence from Gth and Huck(1997)questions whether subjects’preferences for punishment and sacrifce are always motivated by the two assumptions.They argue that some subjects are likely to sacrifice payoffs even without a pecuniary punishment motive andfind evidence that some subjects eliminate an opponent’s payoffat no cost to their own even when the punisher has a favourable proportion of the surplus,which questions wheth
er punishment is restricted to situations that are unfavourable or perceived as‘unfair’.In this paper,we are interested in the extent of such behaviour and investigate how far the existing other-regarding theories can explain the types of behaviour and,if they cannot,what motivates such actions.
To achieve this,we analyxp安装
data from an experiment that was designed to obrve each subject’s behaviour across four games for both roles.Two of the games are the ultimatum and dictator game,and the other two are modified ultimatum games that follow Fellner and Gth(2003)who adapt the payoffs of the ultimatum game such that in the event of a decline the propor and responder receive a-and(1-)-share of their propod payoffs, respectively.Specifically,we focus on the games where=1and=0as in Gth and Huck (1997),which means the games are the same as the ultimatum game except that if an offer is declined,in the former,the responder receives nothing but the propor still receives his propod amount;and in the latter,the responder still receives his propod amount but the propor receives nothing.Notice that when=1there is no pecuniary punishment motive behind a decline,and when=0punishment is cost-free.
Analysing the games in a within-subject design is going to make two main contribu-tions to the other-regarding preference literature.First,it enables us to investigate how far the other-regarding preference literature can explain behaviour in the games at the individual level.To measure this,we
estimate the number of subjects who consistently be-haved as predicted by lf-interest or a prominent other-regarding theory across a number of roles with a reasonable level of er柏洁
ror.The prominent other-regarding theory analyd here is inequality aversion,which forms the basis of the models of Fehr and Schmidt(1999),
2A lf-interested subject should accept any positive offer as responder in the ultimatum game and should keep the entire surplus as propor in the dictato关于习俗的作文
r game.
3For a review of the literature e Fehr and Schmidt(2006).
Bolton and Ockenfels(2000)and Falk and Fischbacher(2006).An inequality aver sub-ject is concerned not only for his material payoffbut also for the equality of an outcome. So,other things equal,the subject prefers others to have the same payoffas him,but he receives some disutility when he is advantageously better offand disadvantageously wor off.The two adapted ultimatum games are particularly adept at testing the assumptions of inequality aversion,becau a willingness to decline positive offers in the=1game highlights that a subject does not have an aversion to disadvantageous inequality,whereas a willingness to decline offers greater than half the surplus in the=0game shows that the subject does not have an aversion to advantageous inequality.Second,t
he within-subject design allows us to analy the correlation of subjects’decisions across roles,which enables us to gain insights into the motives behind subjects’behaviour,if not inequality aversion. This allows us to suggest simple modifications to other-regarding utility functions to cap-ture the behaviour from the games,which may assist any future theoretical work that attempts to explain other-regarding preferences.
Regarding the predictions of inequality aversion,we focus on the model of Fehr and Schmidt(1999)as it is renowned as one of the most tractable of the other-regarding theories which carries a commendable amount of explanatory power in a wide range of games.As with all of the theories,there is some behaviour that it can explain less well.One such example is that it cannot explain why unequal outcomes are more acceptable when offers are generated at random or propors are restricted to unequal offers(e Blount,1995; Nelson,2002;and Falk et al,2008).4In our experiment we do not manipulate the offers available to propors,so the model of Fehr and Schmidt(1999)produces qualitatively similar predictions as intention-bad theories,but it has the benefit that the analysis is not complicated by the subject’s belief of other players’intentions.Another example is that many subjects are unconcerned with equality when participating in pure distribution games,as they em to prefer to maximi the available surplus when reciprocity is not a factor(e
Charness and Rabin,2002;and Engelmann and Strobel,2004).5In this paper we analy behaviour in the dictator game,which Fehr and Schmidt(1999)can describe behaviour well,and the main focus is on games with a clear reciprocal element as oppod to pure distributional games.We discuss how the predictions of Fehr and Schmidt(1999) specifically relate the other theories in Section2.
This paper contributes to a small but growing literature that analys whether sub-jects beha顿号是什么意思
ve as described by other-regarding theories across a number of games.Blanco et al(2007)consider whether the model of Fehr and Schmidt(1999)explains behaviour at the individual level as well as the aggregate level in the ultimatum and dictator game, quential prisoner’s dilemma and public-good game.Their focus differs from the cur-rent paper becau they analy games in which Fehr and Schmidt(1999)can explain well(using between-subject analysis)and,assuming that all subjects are inequality aver, they highlight that inequality aversion performs less well when consistency is considered at the individual level.In contrast,we u the within-subject design to highlight which subjects are unlikely to be inequality aver and investigate the motives behind their be-4This type of behaviour can be explained by Falk and Fischbacher(2006).
5Fehr et al(2006)show that non-economics students are more concerned with equality compared to economics students,who are taught that efficiency is a desirable outcome.
haviour.Brosig et al(2007)investigate subjects’behaviour across distributional games where reciprocity is not a factor.They show that a high share of subjects’behaviour can be described by Charness and Rabin(2002),Fehr and Schmidt(1999)and Andreoni and Miller(2002)across a number of dictator and prisoner’s dilemma games,but theyfind that other-regarding preferences are less prominent over time.
This paper is also related to a number of other studies that have adapted the payoffs of the ultimatum game.Bolton and Zwick’s(1995)impunity game was thefirst to analy subjects’behaviour when a decline only eliminates the responder’s payoff.In their impunity game,offers were restricted to an equal and unequal split in favour of the propor and,in the event of a decline,both players received nothing in the former but only the responder’s payoffis eliminated in the latter.They found that the unequal split was rarely declined, but the focus of their experimental design was on how propors behave;in this paper,we are just as interested,if not more so,in how responders behave.Motivated by Bolton and Zwick’s(1995)impunity game,Gth and Huck(1997)investigated both the=0and=1 games analysing propor and responder behaviour,but in their experiment responders were uncertain of the surplus size.Many of the general results of Gth and Huck(1997) are replicated here,but we analy the games with full information,so we can clearly obrve the ext
ent of subjects’behaviour.We also prent a more detailed comparison of individual behaviour across games and relate the results to the other-regarding preference literature.Fellner and Gth(2003)considered similar games to the ones analyd here but they had=1/6,=1/2and=5/6,which means that asincreas,the cost of punishment decreas and thesp姜刑
strength of punishment increas.They found that there was an increa in rejection rates asincreas but they restricted offers to unequal levels in favour of the propor,so they could not obrve whether responders were willing to decline offers greater than half the stake.6
Bolton and Zwick’s(1995)impunity game is extremely similar to the=1game,so much so that in the literature both have been termed the impunity game and henceforth we follow this convention.7In the abn of a short and catchy name for the=0game, we refer to this as the guarantor game,as a propor guarantees the responder’s拘留所
payoffwhen making an offer.8In the next ction,we provide formal definitions of the impunity and guarantor game and solve for behaviour of lf-interested and strictly inequality aver responders,where the predictions of the latter are ud as the null hypothes of the tests that follow.Section3provides a description of the experimental design in which subjects played games quentially and in a random order to allow them to learn to some extent as the experiment progresd.The results are prented in Section4:Section 4.1gives an overview of subjects’behaviour and shows that many subjects are willing to
6Other papers that are broadly related to this one consider a modified ultimatum game where the propor and responder received a-share of their propod payoffs in the event of a decline,so the strength and cost of the punishment incread with.Suleiman(1996)found that propors’offers significantly incread with,and further investigation by Ahlert et al(2002)and Gth and Kovcs(2002)show that responders are more willing to punish asincreas.Anderoni et al(2003)allow subjects to decide how much they shrink the surplus andfind that offers are lower in this game compared to the standard ultimatum game.
7Compared to Bolton and Zwick’s(1995)impunity game,the=1game is actually a modified impunity game,becau there is a continuous strategy space and the propor always receives his payoffeven if an equal split is declined.
8Fellner and Gth(2003)briefly refer to this as the no-veto-cost game when perhaps the no-cost-veto game would be a clearer description.
increa disadvantageous and advantageous inequality in the impunity and guarantor game, respectively;Section4.2controls for any learning effects and shows that the main results are robust to any such effects;Section4.3estimates that less than30%of subjects behave as if inequality aver an
d less than10%as lf-interested across a number of roles given reasonable error levels;Section4.4considers the correlation between roles and discuss how some other-regarding preferences can be adjusted to capture the behaviour.Section 5concludes.
2Theoretical Predictions
2.1The Games
In each game,there are two players:a propor and responder,who are defined as player1 and2,respectively.They divide a surplus between them,which is normalid to1in this ction.Each game begins with the propor making an offer of x∈[0,1]to the responder. In the dictator game,this proposal is implemented,so the responder receives x and the propor receives1−x.In the other games,the proposal can be accepted or declined. If accepted,the responder receives x and the propor receives1−x.If declined,in the impunity game the responder receives0but the propor receives1−x;in the ultimatum game both players receive0;and in the guarantor game the responder receives x but the propor receives0.
2.2Inequality Aversion
Fehr and Schmidt(1999)show that their model of inequality aversion can predict the robust evidence of the ultimatum and dictator game;that is,it predicts that responders may decline low offers that are less than or equal to half the suplus in the ultimatum game (pp.826),and that propors may offer positive amounts but less than or equal to half the surplus in the dictator game(pp.847).Here we consider the predictions of the model of Fehr and Schmidt(1999)for the impunity and guarantor game.The predictions are ud as the null hypothes of the tests on subjects’behaviour in Section4.
The utility function of Fehr and Schmidt(1999)can be generalid by(1)for a strictly inequality aver player i where only player j is in player i’s reference group.
U i(u i,u i,u i,x i,x j)= u i(x i)−u i(x j−x i)
u i(x i)−u i(x i−x j)if x i≤x j
if x i>x j
(1)
The term u i(x i)is the utility player i receives from a material payoffx i,where∂u i(.)/∂x i> 0and u i(0)=0,
and the terms u i(x i−x j)≥0and u(x j−x i)≥0are player i’s disutility from being better and wor offthan player j,respectively,where x j is player j’s materi科学家小故事
al payoff.When x i≤x j,∂u i(.)/∂x i<0and∂u i(.)/∂x j>0,but when x i>x j,∂u i(.)/∂x i>0and∂u i(.)/∂x j<0.Furthermore,when x i>x j,it is assumed that U i(.)>0and∂U i(.)/∂x i>0,which means that player i is unwilling to discard positive material payoffs to reduce inequality when better offcompared to player j.Finally,it is assumed that u i(x′−x)≥u i(x′−x)where x′>x,which means that for a given distribution
