DO WEALTH DIFFERENCES AFFECT FAIRNESS CONSIDERATIONS?*

The influence of relative wealth on fairness considerations is analyzed in an ultimatum game experiment in which participants receive large and widely unequal initial endowments. Subjects initially demonstrate a concern for fairness. With time however, behavior becomes at odds with both subgame perfection and fairness. Evidence of learning is detected for both proposers and receivers in the estimation of a structural reinforcement learning model. The estimation results suggest that, guided by foregone best responses and an acquired sense of deservingness, rich subjects become more selfish, whereas poor subjects, influenced only by their own experience, learn to tolerate this behavior.     

Bargaining under a deadline: evidence from the reverse ultimatum game

We study a “reverse” ultimatum game, in which proposers have multiple chances to offer responders a division of some fixed pie. The game ends if the responder accepts an offer, or if, following a rejection, the proposer decides not to make a better offer. The unique subgame perfect equilibrium gives the proposer the minimum possible payoff. Nevertheless, the experimental results are not too different from those of the standard ultimatum game, although proposers generally receive slightly less than half of the surplus.We use the reverse ultimatum game to study deadlines experimentally. With a deadline, the subgame perfect equilibrium prediction is that the proposer gets the entire surplus.Deadlines are used strategically to influence the outcome, and agreements are reached near the deadline. Strategic considerations are evident in the differences in observed behavior between the deadline and no deadline conditions, even though agreements are substantially less extreme than predicted by perfect equilibrium.     

On the Irrelevance of Risk Attitudes in Repeated Two-Outcome Games

We study equilibrium and maximin play in supergames consisting of the sequential play of a finite collection of stage games, where each stage game has two outcomes for each player. We show that for two-player supergames in which each stage game is strictly competitive, in any Nash equilibrium of the supergame, play at each stage is a Nash equilibrium of the stage game provided preferences over certain supergame outcomes satisfy a natural monotonicity condition. In particular, equilibrium play does not depend on risk attitudes. We establish an invariance result for games with more than two players when the solution concept is subgame perfection. Journal of Economic Literature Classification Numbers: C72, C9.     

A Note on the Ultimatum Paradox, Bounded Rationality, and Uncertainty

The ultimatum game is a sequential-move bargaining game in which a giver offers a taker a share of a monetary pie. The predicted subgame perfect equilibrium in the ultimatum game is for purely rational givers who act in their own narrow self-interest to offer the smallest possible share of a monetary price, and for purely rational takers to accept. Experimental trials suggest, however, that givers make generous offers because they have a taste for fairness. The analysis presented in this paper argues that it is in the best interest of givers of any type to make offers that will not be rejected, and that offers become more generous as a giver’s uncertainty about the taker’s reservation offer increases.     

“Si él lo necesita”: Gypsy fairness in Vallecas

“Si él lo necesita” (if he really needs it) was the most common argument given by the subjects who accepted the zero offer in the ultimatum game (strategy method) during experiments conducted among illiterate (adult) gypsies in Vallecas, Madrid. Interestingly the acceptance of the zero offer was not a rare case but, in contrast, was the modal value. This is even more remarkable if we consider that the 97% of the subjects proposed the equal split. Electronic Supplementary Material Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s10683-006-9126-0. JEL Classification D63 · D64 · C93 · J15     

Asymmetric Information in Simple Bargaining Games: An Experimental Study

Bilateral bargaining situations are often characterized by informational asymmetries concerning the size of what is at stake: in some cases, the proposer is better informed, in others, it is the responder. We analyze the effects of both types of asymmetric information on proposer behavior in two different situations which allow for a variation of responder veto power: the ultimatum and the dictator game. We find that the extent to which proposers demand less in the ultimatum as compared to the dictator game is (marginally) smaller when the proposer is in the superior information position. Further we find informed proposers to exploit their informational advantage by offering an amount that does not reveal the true size of the pie, with proposers in the ultimatum game exhibiting this behavioral pattern to a larger extent than those in the dictator game. Uninformed proposers risk imposed rejection when they ask for more than potentially is at stake, and ask for a risk premium in dictator games. We concentrate on proposers, but also explore responder behavior: We find uninformed responders to enable proposers’ hiding behavior, and we find proposer intentionality not to play an important role for informed responders when they decide whether to accept or reject an offer by an (uninformed) proposer.     

AN EXPERIMENT WITH ULTIMATUM BARGAINING IN A CHANGING ENVIRONMENT*

We present experimental results on the ultimatum bargaining game which support an evolutionary explanation of subjects’ behaviour in the game. In these experiments subjects interacted with each other and also with virtual players, i.e. computer programs with pre‐specified strategies. Some of these virtual players were designed to play the equitable allocation, while others exhibited behaviour closer to the subgame‐perfect equilibrium, in which the proposer's share is much larger than that of the responder. We have observed significant differences in the behaviour of real subjects depending on the type of “mutants” (virtual players) that were present in their environment.     

Reciprocity—an indirect evolutionary analysis

This paper investigates agents who face a stylized pecuniary ‘game of life’ comprising the ultimatum game and the dictator game. Utility may but need not be attached to equity and reciprocity, as formalized by Falk and Fischbacher (Games Econom Behav, 54(2): 293–315, 2006) but, critically, this social component of preferences cannot be conditioned on whether an ultimatum or a dictator game is played. Evolutionary fitness of agents is determined solely by material success. Under these conditions, a strong preference for reciprocity, but little interest in equity as such evolves. Possible exogenous constraints that link reciprocity and equity concerns imply long-run levels of both which depend on the relative frequency of ultimatum vs. dictator interaction in agents’ multi-game environment. Financial support from the German Academic Exchange Service (DAAD) is gratefully acknowledged.     

Are we nice(r) to nice(r) people?—An experimental analysis

We experimentally investigate whether individuals can reliably detect cooperators (the nice(r) people) in an anonymous decision environment involving “connected games.” Participants can condition their choices in an asymmetric prisoners’ dilemma and a trust game on past individual (their partner’s donation share to a self-selected charity) and social (whether their partner belongs to a group with high or low average donations) information. Thus, the two measures of niceness are the individual donation share in the donation task, and the cooperativeness of one’s choice in the two games. We find that high donors achieve a higher-than-average expected payoff by cooperating predominantly with other high donors. Group affiliation proved to be irrelevant. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C91, C72, D3     

The Ultimatum Game: Optimal Strategies without Fairness

The ultimatum game is simple and this facilitates its use in the study of predictions of game theory. Experimental evidence suggests that it does not predict individual behavior well, unless individuals gain welfare from fairness in transactions, or have expectations about some wider game. Our model excludes any notion of fairness by including (potential) rivalry in transactions. In this game the proposer's expectations yield outcomes that are consistent with experimental evidence. Offers can be large or small, with none in an intermediate range. The consequent distribution appears in dictator game experiments. Our model explains how it is generated by expectations.Journal of Economic LiteratureClassification Numbers: C72, D82, D84.     

Competition for Power and Altruism

The paper analyzes the trade-off between power and altruism by using an experimental framework which involved a group of experimental agents, undergraduate students of the University of Siena. The results show that the introduction into the experimental structure of a tournament for the power appreciably altered the behaviour of agents. More specifically the degree of altruism, measured by the dictator offers, significantly decreased when the agents were able to trade altruism for power. The results were more clear-cut and robust in the case of the dictator game, but also in the case of the ultimatum game the introduction of the tournament for power altered the behavior of subjects. A significant gender effect emerged.     

A stress test of fairness measures in models of social utility

Summary. Current social utility models posit fairness as a motive for certain types of strategic behavior. The models differ, however, with respect to how fairness is measured. Distribution models measure fairness in terms of relative payoff comparisons. Reciprocal-kindness models measure fairness in terms of gifts given and gifts received. Reference points play an important role in both measures, but the reference points in reciprocal-kindness models are conditioned on the actions available to players, whereas those in distributive models are not. Data from an ultimatum game experiment that stress tests the kindness measure is consistent with the distributive measure. Data from an experiment that stress tests the distributive measure is inconsistent with the distributive measure, but moves in the direction opposite that implied by the kindness measure. A measure that combines relative payoff comparisons with a reference point conditioned on feasible actions provides a first approximation to our data.Received: 12 August 2002, Revised: 27 November 2003, JEL Classification Numbers: C78, C91, D63. Correspondence to: Axel OckenfelsBolton gratefully acknowledges the support of the National Science Foundation. Ockenfels thanks Alvin Roth and the Harvard Business School for their generous hospitality, and the Deutsche Forschungsgemeinschaft for their support through the Emmy Noether-program. Both authors gratefully acknowledge the hospitality of the Making Choices project at the Center for Interdisciplinary Research, University of Bielefeld during the summer of 2000. We also thank an anonymous referee and seminar participants in Bielefeld, Boston, Columbus, Harvard, and Jena for helpful comments.     

On the interpretation of bribery in a laboratory corruption game: moral frames and social norms

Past studies on laboratory corruption games have not been able to find consistent evidence that subjects make “immoral” decisions. A possible reason, and also a critique of laboratory corruption games, is that the experiment may fail to trigger the intended immorality frame in the minds of the participants, leading many to question the very raison d’être of laboratory corruption games. To test this idea, we compare behavior in a harassment bribery game with a strategically identical but neutrally framed ultimatum game. The results show that fewer people, both as briber and bribee, engage in corruption in the bribery frame than in the alternative and the average bribe amount is lesser in the former than in the latter. These suggest that moral costs are indeed at work. A third treatment, which relabels the bribery game in neutral language, indicates that the observed treatment effect arises not from the neutral language of the ultimatum game but from a change in the sense of entitlement between the bribery and ultimatum game frames. To provide further support that the bribery game does measure moral costs, we elicit the shared perceptions of appropriateness of the actions or social norm, under the two frames. We show that the social norm governing the bribery game frame and ultimatum game frame are indeed different and that the perceived sense of social appropriateness plays a crucial role in determining the actual behavior in the two frames. Furthermore, merely relabelling the bribery game in neutral language makes no difference to the social appropriateness norm governing it. This indicates that, just as in the case of actual behavior, the observed difference in social appropriateness norm between bribery game and ultimatum game comes from the difference in entitlement too. Finally, we comment on the external validity of behavior in lab corruption games.     

More Is Better, But Fair Is Fair: Tipping in Dictator and Ultimatum Games

This paper examines Allocators' willingness to reward and punish their paired Recipients. Recipients only compete in a skill-testing contest, the outcome of which determines the size of the surplus. In the dictator game, Allocators reward skillful Recipients, but punish unskillful ones only modestly. The punishment effect is mitigated by the belief held by some Allocators thateffortis the appropriate measure of deservingness. The ultimatum game extension reveals offerers' ability to adapt to the strategic environment. Offers to skillful Recipients in the ultimatum game, however, are shown to be motivated by a taste for fairness, and not strategic considerations.Journal of Economic LiteratureClassification Numbers: C70, C91, D63.     

Relative versus Absolute Speed of Adjustment in Strategic Environments: Responder Behavior in Ultimatum Games

Learning models predict that the relative speed at which players in a game adjust their behavior has a critical influence on long term behavior. In an ultimatum game, the prediction is that proposers learn not to make small offers faster than responders learn not to reject them. We experimentally test whether relative speed of learning has the predicted effect, by manipulating the amount of experience accumulated by proposers and responders. The experiment allows the predicted learning by responders to be observed, for the first time.     

Fairness and intentionality in children’s decision-making

Few studies have addressed the role of different aspects of the Theory of Mind (ToM) (intentionality and false belief understanding) in decision-making by adults playing strategic games where the importance of fairness is crucial. Even more interesting, this topic has been less investigated with children. The goal of this research was to explore the development of the decisional behavior along with the understanding of fairness, intentions and first- and second-order false belief understanding in children who are just acquiring those abilities. Multiple rounds of the ultimatum game with a human and a non-human partner (child/roulette wheel) were played by 177 children in the age range of 5–10 years, who also completed classic false belief tasks. Results confirm the key role of fairness sensibility across age groups and different degrees of the relevance of ToM according to the variability of children’s decisional behavior (stable vs. dynamic).     

From ultimatum to Nash bargaining: Theory and experimental evidence

We consider a sequential two-party bargaining game with uncertain information transmission. When the first mover states her demand she does only know the probability with which the second mover will be informed about it. The informed second mover can either accept or reject the offer and payoffs are determined as in the ultimatum game. Otherwise the uninformed second mover states his own demand and payoffs are determined as in the Nash demand game. In the experiment we vary the commonly known probability of information transmission. Our main finding is that first movers’ and uninformed second movers’ demands adjust to this probability as qualitatively predicted, that is, first movers’ (uninformed second movers’) demands are lower (higher) the lower the probability of information transmission. JEL Classification C72 · C78 · C92     

Incentive effects and overcrowding in tournaments: An experimental analysis

This study reports experiments that examine outcomes when agents choose between a payment scheme that rewards based on absolute performance (i.e., piece rate) and a scheme that rewards based on relative performance (i.e., a tournament). Holding total payments in the tournament constant, performance is higher when the tournament option is winner-take-all compared to a graduated tournament (i.e., second and third-place performers also receive a payment). Performance is higher in the winner-take all tournaments even among participants that choose the piece-rate option. While there is a modest amount of overcrowding, there are no significant differences in overcrowding across conditions. Entry rates into the tournament and the relative ability of tournament entrants (compared to non-entrants in the same condition) are higher in the graduated tournament condition than the winner-take-all conditions. Consequently, the winner-take-all tournament is more efficient than the graduated tournament (incentive effects are stronger and the overcrowding is about the same), but the graduated tournament provides a more effective mechanism to identify the most capable performer in a talent pool. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification D8 · J3 · L2     

Subgame Perfect Equilibria in Stage Games

It is well known that a stage game with infinite choice-sets, unless it contains a public coordination-device in each stage, may have no subgame perfect equilibria. We show that if a game with public coordination-devices has a subgame perfect equilibrium in which two players in each stage use non-atomic strategies, then the game without coordination devices also has a subgame perfect equilibrium. Journal of Economic Literature Classification Numbers: C6, C7, D8.     

Information acquisition in the ultimatum game: An experimental study

We experimentally investigate if free information disadvantages a player relative to when information is unavailable. We study an Ultimatum game where the Proposer, before making an offer, can obtain free information about the Responder's minimum acceptable offer. Theoretically, the Proposer should obtain the information and play a best reply to the Responder's minimum acceptable offer. Thus the Responder should get the largest share of the surplus. We find that an increasing number of Proposers become informed over time. Moreover, the proportion of Proposers who use the information to maximize money earnings increases over time. The majority of information-acquiring Proposers, however, refuse to offer more than one-half and play a best reply only to Responders who accept offers of one-half or less. This, together with a substantial proportion of Proposers who choose to remain uninformed, means that the availability of free information backfires for Proposers only by a little. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C70, D63, D80