Reciprocity and Giving in a Consecutive Three‐Person Dictator Game with Social Interaction

We study pure indirect reciprocity by setting up a modified dictator game with three players A, B, and C acting sequentially. Subject A takes a share of a pie and passes the rest to subject B, while B divides the rest between herself and C. We find that this consecutive three‐person dictator game increases generosity compared with the traditional two‐person dictator game. We analyze the influence of social interaction and uncertainty. In treatments with certainty we observe pure indirect reciprocity: B indirectly reciprocates for A's behavior in the decision on how generous to be to C.     

Reputation and Reciprocity: Consequences for the Labour Relation

Recent evidence highlights the importance of social norms in many economic relations. However, many of these relationships are long term and provide repeated game incentives for performance. We experimentally investigate interaction effects of reciprocity and repeated game incentives in two treatments (one-shot and repeated) of a gift-exchange game. In both treatments we observe reciprocity, which is strengthened in the repeated game. A detailed analysis shows that, in the repeated game, some subjects imitate reciprocity. Thus, reciprocity and repeated game incentives reinforce each other. Observed behaviour is robust against experience. We conclude that long-term interaction is a "reciprocity-compatible" contract enforcement device.
JEL classification : J 30; C 91     

Social norms, information, and trust among strangers: theory and evidence

Can a social norm of trust and reciprocity emerge among strangers? We investigate this question by examining behavior in an experiment where subjects repeatedly play a two-player binary “trust” game. Players are randomly and anonymously paired with one another in each period. The main questions addressed are whether a social norm of trust and reciprocity emerges under the most extreme information restriction (anonymous community-wide enforcement) or whether trust and reciprocity require additional, individual-specific information about a player’s past history of play and whether that information must be provided freely or at some cost. In the absence of such reputational information, we find that a social norm of trust and reciprocity is difficult to sustain. The provision of reputational information on past individual decisions significantly increases trust and reciprocity, with longer histories yielding the best outcomes. Importantly, we find that making reputational information available at a small cost may also lead to a significant improvement in trust and reciprocity, despite the fact that most subjects do not choose to purchase this information.     

Implications of trust, fear, and reciprocity for modeling economic behavior

This paper reports three experiments with triadic or dyadic designs. The experiments include the moonlighting game in which first-mover actions can elicit positively or negatively reciprocal reactions from second movers. First movers can be motivated by trust in positive reciprocity or fear of negative reciprocity, in addition to unconditional other-regarding preferences. Second movers can be motivated by unconditional other-regarding preferences as well as positive or negative reciprocity. The experimental designs include control treatments that discriminate among actions with alternative motivations. Data from our three experiments and a fourth one are used to explore methodological questions, including the effects on behavioral hypothesis tests of within-subjects vs. across-subjects designs, single-blind vs. double-blind payoffs, random vs. dictator first-mover control treatments, and strategy responses vs. sequential play. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C70, C91, D63, D64     

Reciprocity Game

This paper shows that reciprocity comes from the desire to cooperate in finitely repeated prisoner's dilemma game. Before playing the finitely repeated prisoner's dilemma game, players choose the reciprocity level and commit to it, and the reciprocity level is public information. There are T equilibria if the prisoner's dilemma game is repeated for T periods, and each equilibrium is associated with different levels of cooperation. Further, if players choose their reciprocity levels sequentially, then the most cooperative equilibrium will be the unique equilibrium. However, reciprocity does not matter for the one‐period game and the infinitely repeated game.     

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.     

Trust and trustworthiness in games: An experimental study of intergenerational advice

This paper investigates the development of conventions of trust in what we call intergenerational games, i.e., games played by a sequence of non-overplapping agents, who pass on advice on how to play the game across adjacent generations of players. Using the trust game of Berg et al. (1995) as our experimental decision problem, advice seems to decrease the amount of trustthat evolves when this game in played in an inter-generational manner in that it decreases the amount of money sent from Senders to Returners. Ironically, advice increases trustworthinessin that Returners tend to send more back. Further, subjects appear to follows conventions of reciprocity in that they tend to Send more if they think the Returners acted in a “kind” manner, where kind means the Sender sent more money than the receiver expected. Finally, while we find a causal relationship running from trustworthiness to trust, the opposite can not be established. We note that many of our results can only be achieved using the tools offered by inter-generational games. The inter-generational advice offered provides information not available when games are played in their static form. Combining that information with elicited beliefs of the Senders and Returners adds even more information that can be used to investigate the motives that subjects have for doing what they do. Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users. JEL Classification C91 · C72 Resources for this research were provided by National Science Foundation grants SBR-9709962 and SBR-9709079 and by both the Center for Experimental Social Science and the C.V. Starr Center for Applied Economics at New York University. We would like to thank Shachar Kariv for both his comments and research assistance. We also thank Mikhael Shor and Judy Goldberg for research assistance, and Yevgeniy Tovshteyn for computer programming.     

Multilateral tariff cooperation under fairness and reciprocity

Abstract This paper explores the impact of fairness and reciprocity on multilateral tariff cooperation. Reciprocal countries reward kind behaviour (positive reciprocity), but retaliate against countries behaving unkindly (negative reciprocity). We demonstrate that reciprocal countries that are moderately demanding from their trading partners regarding their commercial policy can support a greater degree of cooperation than self‐interested ones. However, when only very liberal import policies are considered fair, then reciprocity could have a detrimental effect on multilateral tariff cooperation.Thus, our model provides a novel perspective on the role of expectations in trade negotiations.     

A Bayesian Model of Voting in Juries

We model voting in juries as a game of incomplete information, allowing jurors to receive a continuum of signals. We characterize the unique symmetric equilibrium of the game, and give a condition under which no asymmetric equilibria exist under unanimity rule. We offer a condition under which unanimity rule exhibits a bias toward convicting the innocent, regardless of the size of the jury, and give an example showing that this bias can be reversed. We prove a “jury theorem” for our general model: As the size of the jury increases, the probability of a mistaken judgment goes to zero for every voting rule except unanimity rule. For unanimity rule, the probability of making a mistake is bounded strictly above zero if and only if there do not exist arbitrarily strong signals of innocence. Our results explain the asymptotic inefficiency of unanimity rule in finite models and establishes the possibility of asymptotic efficiency, a property that could emerge only in a continuous model. Journal of Economic Literature Classification Numbers: C72, D72.     

A theory of sequential reciprocity

Many experimental studies indicate that people are motivated by reciprocity. Rabin [Amer. Econ. Rev. 83 (1993) 1281] develops techniques for incorporating such concerns into game theory and economics. His theory is developed for normal form games, and he abstracts from information about the sequential structure of a strategic situation. We develop a theory of reciprocity for extensive games in which the sequential structure of a strategic situation is made explicit, and propose a new solution concept—sequential reciprocity equilibrium—for which we prove an equilibrium existence result. The model is applied in several examples, and it is shown that it captures very well the intuitive meaning of reciprocity as well as certain qualitative features of experimental evidence.     

Trust and reciprocity in inter-individual versus inter-group interactions: The effects of social influence, group dynamics, and perspective biases

Using an experimental trust game, I examine whether the perspectives and behavior of group representatives and consensus groups differ from those of the same individuals in an analogous inter-individual situation. A primary goal of this research is to extend past work on trust and reciprocity by examining the impact of the social contexts within which social interactions are characteristically embedded. Specifically, this research concerns whether norms and dynamics of trust and reciprocity differ in the contexts of inter-individual and inter-group interactions. First, I examine whether dynamics of trust and reciprocity differ in various inter-group interactions where inter-group decisions are operationalized as 1) autonomous group representatives, i.e., individuals who are given the responsibility of unilaterally making a decision on behalf of a three-person group engaging with a group representative of another such group; and 2) consensus groups, i.e., group members making a consensus trust or reciprocity decision for their groups via a collective process with another such group. Results of these studies show that 1) people trust less and reciprocate less when responsible for a group or organizational decision as autonomous group representatives; 2) consensus groups do not differ from individuals in their level of trust but show dramatically less reciprocity. The group consensus mechanism in fact produced by far the lowest reciprocity level, significantly lower than that exhibited by either individuals or autonomous group representatives. Thus, inter-group trust and reciprocity dynamics are not readily inferable from their inter-individual counterparts. Moreover, an important implication is emerging here: the extent and direction of the discrepancy between individual and group choices in regard to trust and reciprocity levels and possibly other social preferences in general may depend importantly on the precise details of the group decision-making mechanism, for example whether decisions are made consensually, by majority vote, or by a group leader or representative. In addition to examining the level of trust and reciprocity that occur in these various situations, I also studied, using both behavioral and questionnaire data, the roles of self-interest, social influence, and group dynamics in trust and reciprocity perceptions and behavior. The results showed that there exist discrepancies between behavioral forecasts and the actual behavior, and that trusting behavior is driven strongly by expectation of level of reciprocation, while reciprocating behavior is driven strongly by the difference between trust expectation and actual trust received.     

Dynamic psychological games

The motivation of decision makers who care for various emotions, intentions-based reciprocity, or the opinions of others may depend directly on beliefs (about choices, beliefs, or information). Geanakoplos, Pearce and Stacchetti [J. Geanakoplos, D. Pearce, E. Stacchetti, Psychological games and sequential rationality, Games Econ. Behav. 1 (1989) 60-79] point out that traditional game theory is ill-equipped to address such matters, and they pioneer a new framework which does. However, their toolbox - psychological game theory - incorporates several restrictions that rule out plausible forms of belief-dependent motivation. Building on recent work on dynamic interactive epistemology, we propose a more general framework. Updated higher-order beliefs, beliefs of others, and plans of action may influence motivation, and we can capture dynamic psychological effects (such as sequential reciprocity, psychological forward induction, and regret) that were previously ruled out. We develop solution concepts, provide examples, explore properties, and suggest avenues for future research.     

Purification, saturation and the exact law of large numbers

Purification results are important in game theory and statistical decision theory. We prove a new purification theorem that generalizes several earlier results. The key idea of our proof is to make use of the exact law of large numbers. As an application, we show that every mixed strategy in games with finite players, general action spaces and diffused, conditionally independent incomplete information has many strong purifications.     

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.     

Cooperation in a risky world

We offer a novel investigation of the effect of environmental risk on cooperation in the Voluntary Contribution Mechanism. Our baseline is the standard setting, in which the personal return from the public good is deterministic, homogeneous, and publicly known. Our experimental treatments alter this classic design by making the marginal per capita return from the public good probabilistic. In the homogeneous risk (HomR) treatment, the random draw is made for the whole group, whereas in the heterogeneous risk (HetR) treatment, this happens independently for each group member. Our hypothesis is that different environmental risks may differently affect the ex post payoff inequalities, so that other‐regarding preferences (inequality aversion) may generate higher contributions in HomR than in HetR. Our main result is that the environmental risk does not affect the patterns of cooperation either in the one‐shot or in the finitely repeated version of the game. This suggests that the standard experimental methodology provides a robust and conservative measure of human cooperation.     

Game Theory via Revealed Preferences

We investigate equilibrium notions in game theory from the revealed preference approach. For extensive game forms with complete information, we derive a set of independent necessary and sufficient conditions for the observed outcomes to be rationalized by subgame-perfect Nash equilibrium. Journal of Economic Literature Classification Numbers: C72, C92.     

关于强互惠及政府型强互惠理论的研究

美国Santa Fe研究所的经济学家的研究表明,群体中自发的强互惠的出现,保证了合作在群体内的延续,从而使得群体成功演化.在此基础上,进一步认为 ,强互惠者的职业化以及政府型强互惠能更有效地对不合作者实施制裁,于是合作在强制下使得社会成为可能.     

POLITICAL INEQUALITY,CENTRALIZED SANCTIONING INSTITUTIONS,AND THE MAINTENANCE OF PUBLIC GOODS

Centralized sanctioning institutions cultivate cooperation by eradicating the gains from free‐riding. Studies show that electing a community member to operate a centralized sanctioning institution further increases support for the public good. These studies have overlooked an all‐too‐common attribute of non‐laboratory elections: political inequality. In this paper, we replicate those studies and, then, introduce novel experimental treatments that examine how political inequality influences the cooperation‐enhancing effect of a democratic election to centralized sanctioning institutions. In our novel treatment conditions, participants receive either a random allotment of votes that they can use to elect a centralized sanctioning authority or an allocation of votes proportional to their earnings in a previously‐executed public goods game. We find that political inequalities created via the random allocation of votes do not hinder cooperation, whereas political inequalities created via past game play undermine elected authorities and diminish contributions to the public good from individuals advantaged by political inequality.     

Social division,trust, and reciprocity among Chinese inmates

Social capital promotes cooperation between people and, in turn, economic growth and stability. Trust and trustworthiness are components of social capital that are associated with economic success. This paper provides insight into the impact of social division on cooperative behavior. We use the one-shot investment game to measure trust and reciprocity among inmates in a Chinese prison, which offers an institutional setting that allows us to examine how social interaction, or a lack thereof, fosters cooperation. Results show that the variation in social division through physical separation does not have a significant impact on cooperative behavior among inmates. However, inmates are more trusting than our benchmark group of university students even though inmates have faced significant life challenges. While social interaction fails to boost trust and reciprocity, childhood experience and family environment mold social preferences. In particular, reciprocity deteriorates for those who have migrant mothers.     

Breaking the norm: An empirical investigation into the unraveling of good behavior

We present results from an artefactual field experiment conducted in rural Peru that considers whether observing non-reciprocal behavior influences an individual's decision to reciprocate. Specifically, we consider the behavior of second movers in a trust game, assessing whether their decision to reciprocate is influenced by the observed reciprocity of others. In documenting the impact of an external shock to observed reciprocity, this paper shows that small increases in non-reciprocal behavior result in an unraveling of the norm of reciprocity. Survey data is used to explore mechanisms by which this occurred. Results are not consistent with learning effects, suggesting that preferences may be changed by observing others deviating from a norm of reciprocity. These results suggest that investing in encouraging trustworthy behavior can have large benefits in situations where individuals are observing each other's behavior, such as may be the case in a new market institution.