A theory of reciprocity

People are reciprocal if they reward kind actions and punish unkind ones. In this paper we present a formal theory of reciprocity. It takes into account that people evaluate the kindness of an action not only by its consequences but also by its underlying intention. The theory is in line with the relevant stylized facts of a wide range of experimental games, such as the ultimatum game, the gift-exchange game, a reduced best-shot game, the dictator game, the prisoner's dilemma, and public goods games. Furthermore, it predicts that identical consequences trigger different reciprocal responses in different environments. Finally, the theory explains why outcomes tend to be fair in bilateral interactions whereas extremely unfair distributions may arise in competitive markets.     

The Impact of Exchange Context on the Activation of Equity in Ultimatum Games

In this paper we report the results of additional exchange ultimatum game experiments conducted at the same time as the exchange ultimatum game experiments reported in Hoffman et al. (Games and Economic Behavior, 7(3), pp. 346–380, 1994). In these additional experiments, we use instructions to change an impersonal exchange situation to a personal exchange situation. To do this, we prompt sellers to consider what choices their buyers will make. Game theory would predict that thinking about the situation would lead sellers to make smaller offers to buyers. In contrast, we find a significant increase in seller offers to buyers. This result suggests that encouraging sellers to thinking about buyer choices focuses their attention on the strategic interaction with humans who think they way they do in personal exchange situations, and who may punish them for unacceptable behavior, and not on the logic of the game theoretic structure of the problem.     

Preferences, Property Rights, and Anonymity in Bargaining Games

Research on ultimatum and dictator games has found that because of "fairness" first movers in such games offer more than noncooperative game theory predicts. We find that if the right to be the first mover is "earned" by scoring high on a general knowledge quiz, then first movers behave in a more self-regarding manner. We also conducted dictator double blind experiments, in which the experimenter could not identify the decision maker. The results yielded by far our largest observed incidence of self-regarding offers, suggesting that offers are due to strategic and expectation considerations. Journal of Economic Literature Classification Numbers: C78, C91.     

How Proper Is Sequential Equilibrium?

A strategy profile of a normal form game is proper if and only if it is quasi-perfect in every extensive form (with that normal form). Thus, properness requires optimality along a sequence of supporting trembles, while sequentiality only requires optimality in the limit. A decision-theoretic implementation of sequential rationality, strategic independence respecting equilibrium (SIRE), is defined and compared to proper equilibrium, using lexicographic probability systems. Finally, we give tremble-based characterizations, which do not involve structural features of the game, of the rankings of strategies that underlie proper equilibrium and SIRE.Journal of Economic LiteratureClassification Numbers: C70, C72.     

Of mice and men: Within gender variation in strategic behavior

We study behavioral differences across and within genders in a family of ultimatum and dictator games. We find these differences are due not only to altruistic preferences but also beliefs about the strategic behavior of others. The behavior of men in strategic situations is not significantly more aggressive than women on average. But this average masks wide variation in intra-gender behavior. In particular, a sizable minority of males are “mice,” behaving timidly in strategic environments. Our experimental design shows that the standard ultimatum game can mask significant inter- and intra-gender differences in strategic behavior. These behavioral patterns in strategic environments are shown to be correlated with preferences for altruism in non-strategic settings. Such gender differences could well manifest themselves in real-world large-stakes transactions, such as salary negotiations.     

To Commit or Not to Commit: Endogenous Timing in Experimental Duopoly Markets

In this paper we experimentally investigate the extended game with action commitment of Hamilton and Slutsky (1990, Games Econ. Behavior2, 29–46). In their duopoly game firms can choose their quantities in one of two periods before the market clears. If a firm commits to a quantity in period 1, it does not know whether the other firm also commits early. By waiting until period 2, a firm can observe the other firm's period-1 action. Hamilton and Slutsky predicted the emergence of endogenous Stackelberg leadership. Our data, however, do not confirm the theory. While Stackelberg equilibria are extremely rare, we often observe endogenous Cournot outcomes and sometimes collusive play. This is partly driven by the fact that endogenous Stackelberg followers learn to behave in a reciprocal fashion over time, i.e., they learn to reward cooperation and to punish exploitation. Journal of Economic Literature Classification Numbers: C72, C92, D43.     

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.     

Of mice and men: Within gender variation in strategic behavior

We study behavioral differences across and within genders in a family of ultimatum and dictator games. We find these differences are due not only to altruistic preferences but also beliefs about the strategic behavior of others. The behavior of men in strategic situations is not significantly more aggressive than women on average. But this average masks wide variation in intra-gender behavior. In particular, a sizable minority of males are “mice,” behaving timidly in strategic environments. Our experimental design shows that the standard ultimatum game can mask significant inter- and intra-gender differences in strategic behavior. These behavioral patterns in strategic environments are shown to be correlated with preferences for altruism in non-strategic settings. Such gender differences could well manifest themselves in real-world large-stakes transactions, such as salary negotiations.     

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.     

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.     

Mixing the carrots with the sticks: third party punishment and reward

While the opportunity to punish selfish and reward generous behavior coexist in many instances in daily life, in most laboratory studies, the demand for punishment and reward are studied separately from one another. This paper presents the results from an experiment measuring the demand for reward and punishment by ‘unaffected’ third parties, separately and jointly. We find that the demand for costly punishment is substantially lower when individuals are also given the ability to reward. Similarly, the demand for costly reward is lower when individuals can also punish. The evidence indicates the reason for this is that costly punishment and reward are not only used to alter the material payoff of others as assumed by recent economic models, but also as a signal of disapproval and approval of others’ actions, respectively. When the opportunity exists, subjects often choose to withhold reward as a form of costless punishment, and to withhold punishment as a form of costless reward. We conclude that restricting the available options to punishing (rewarding) only, may lead to an increase in the demand for costly punishment (reward).     

On the Relationship between Risk-Dominance and Stochastic Stability

In a 2 × 2 symmetric game with two symmetric equilibria, one risk-dominates another if and only if the equilibrium strategy is a unique best response to any mixture that gives itself at least a probability of one-half. In a two-person strategic form game, we call a Nash equilibriumglobally risk-dominantif it consists of strategies such that each one of them is a unique best response to any mixture that gives the other at least a probability of one-half. We show that if a weakly acyclic two-person game has a globally risk-dominant equilibrium, then this is the one that is selected by the stochastic equilibrium selection process of Young.Journal of Economic LiteratureClassification Numbers: C72, C73.     

Testing subgame perfection apart from fairness in ultimatum games

We present an experiment designed to separate the two commonplace explanations for behavior in ultimatum games—subjects’ concern for fairness versus the failure of subgame perfection as an equilibrium refinement. We employ a tournament structure of the bargaining interaction to eliminate the potential for fairness to influence behavior. Comparing the results of the tournament game with two control treatments affords us a clean test of subgame perfection as well as a measure fairness-induced play. We find after 10 iterations of play that about half of all non-subgame-perfect demands are due to fairness, and the rest to imperfect learning. However, as suggested by models of learning, we also confirm that the ultimatum game presents an especially difficult environment for learning subgame perfection. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C91, D64, J52     

Imitation and selective matching in reputational games

This paper investigates imitation and selective matching in reputational games with an outside option. We identify two classes of such games, ultimatum and trust games. By selective matching we mean that short-run players have the possibility of selecting the long-run player they play against. We find that selective matching (unlike random matching) favors the equilibrium associated to reputation in the ultimatum game, but not in the trust game.     

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     

The Envelope Theorem and Comparative Statics of Nash Equilibria

The Envelope Theorem for Nash equilibria shows that the strategic reaction of the other players in the game is important for determining how parameter perturbations affect a given player's indirect objective function. The fundamental comparative statics matrix of Nash equilibria for theithplayer in anN-player static game includes the equilibrium response of the otherN−1players in the game to the parameter perturbation and is symmetric positive semidefinite subject to constraint. This result is fundamental in that it holds for all sufficiently smooth Nash equilibria and is independent of any curvature or stability assumptions imposed on the game.Journal of Economic LiteratureClassification Numbers: C72, C61.     

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.     

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.     

Inter-gender interaction and communication in ultimatum games

In this article, we focus on bargaining within male–female pairs, the most pervasive partnership in humankind. We analyse data from an ultimatum game played by Greek participants. Parallel to this, we introduce a one-way communication protocol according to which the responders can send short messages to the receivers, after making their decisions. The analysis shows that gender and message effects exist and males are more effective bargainers.