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.     

Indirect reciprocity and strategic reputation building in an experimental helping game

We study indirect reciprocity and strategic reputation building in an experimental helping game. At any time only half of the subjects can build a reputation. This allows us to study both pure indirect reciprocity that is not contaminated by strategic reputation building and the impact of incentives for strategic reputation building on the helping rate. We find that pure indirect reciprocity exists, but also that the helping decisions are substantially affected by strategic considerations. Finally, we find that strategic do better than non-strategic players and non-reciprocal do better than reciprocal players, casting doubt on previously proposed evolutionary explanations for indirect reciprocity.     

Indirect reciprocity and strategic reputation building in an experimental helping game

We study indirect reciprocity and strategic reputation building in an experimental helping game. At any time only half of the subjects can build a reputation. This allows us to study both pure indirect reciprocity that is not contaminated by strategic reputation building and the impact of incentives for strategic reputation building on the helping rate. We find that pure indirect reciprocity exists, but also that the helping decisions are substantially affected by strategic considerations. Finally, we find that strategic do better than non-strategic players and non-reciprocal do better than reciprocal players, casting doubt on previously proposed evolutionary explanations for indirect reciprocity.     

Self-selection and the power of incentive schemes: an experimental study

We examine how self-selection of workers depends on the power of incentive schemes and how it affects team performance if the power of the incentive schemes is increased. In a laboratory experiment, we let subjects choose between (low-powered) team incentives and (high-powered) individual incentives. We observe that subjects exhibiting high trust or reciprocity in the trust game are more likely to choose team incentives. When exposed to individual incentives, subjects who chose team incentives perform worse if both the unobservable interdependency between their efforts and their incentive to cooperate under team incentives are high.     

Learning, teaching, and turn taking in the repeated assignment game

History-dependent strategies are often used to support cooperation in repeated game models. Using the indefinitely repeated common-pool resource assignment game and a perfect stranger experimental design, this paper reports novel evidence that players who have successfully used an efficiency-enhancing turn taking strategy will teach other players in subsequent supergames to adopt this strategy. We find that subjects engage in turn taking frequently in both the Low Conflict and the High Conflict treatments. Prior experience with turn taking significantly increases turn taking in both treatments. Moreover, successful turn taking often involves fast learning, and individuals with turn taking experience are more likely to be teachers than inexperienced individuals. The comparative statics results show that teaching in such an environment also responds to incentives, since teaching is empirically more frequent in the Low Conflict treatment with higher benefits and lower costs.     

Reciprocity, Trust, and Payoff Privacy in Extensive Form Bargaining

We report decision making in two-person extensive form game trees, using six treatments that vary matching protocol, payoffs, and payoff information. Our objective is to examine game theoretic hypotheses of decision making based on dominance and backward induction in comparison with the culturally or biologically derived hypothesis that reciprocity supports more cooperation than predicted by game theory. We find strong support for cooperation under complete information, even in single-play treatments and in games of trust, unreinforced by the prospect of punishment for defection from reciprocity. Only under private information do we observe strong support for noncooperative game theory.Journal of Economic LiteratureClassification Numbers: C78, C92.     

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.     

Reciprocity under moral wiggle room: Is it a preference or a constraint?

We analyze reciprocal behavior when moral wiggle room exists. Dana et al. (Econ Theory 33(1):67–80, 2007) show that giving in a dictator game is inconsistent with distributional preferences as the giving rate drops when situational excuses for selfish behavior are provided. Our binary trust game closely follows their design. Only a preceding stage (safe outside option vs. enter the game) is added in order to introduce reciprocity. We find significantly lower rates of selfish choices in the trust baseline in comparison to our treatments that feature moral wiggle room manipulations and a dictator baseline. It seems that reciprocal behavior is not only due to people liking to reciprocate but also because they feel obliged to do so.     

Collusive behaviour in finite repeated games with bonding

In finite repeated games, it is not possible to enforce collusive behaviour using deterrent strategies if the state game has a unique Nash equilibrium, because of the ‘unravelling’ of cooperative behaviour in the last period. This paper demonstrates that under certain conditions, some cooperation among the players can be maintained if they can post a bond which they must forfeit if they defect from the cooperative mode. We show that the incentives to cooperate increase as the period of interaction grows in that the size of the bonds required to deter defection become arbitrarily small as the number of periods in the game increases.     

Social norms and trust among strangers

We study the development of a social norm of trust and reciprocity among a group of strangers via the “contagious strategy” as defined in Kandori (1992). Over an infinite horizon, the players anonymously and randomly meet each other and play a binary trust game. In order to provide the investors with proper incentives to follow the contagious strategy, there is a sufficient condition that requires that there exists an outside option for the investors. Moreover, the investorsʼ payoff from the outside option must converge to the payoff from trust and reciprocity as the group size goes to infinity. We show that this sufficient condition is also a necessary condition to sustain any sequential equilibrium in which the trustees adopt the contagious strategy. Our results imply that a contagious equilibrium only supports trust if trust contributes almost nothing to the investorsʼ payoffs.     

Communication in dynastic repeated games: ‘Whitewashes’ and ‘coverups’

Summary. We ask whether communication can directly substitute for memory in dynastic repeated games in which short lived individuals care about the utility of their offspring who replace them in an infinitely repeated game. Each individual is unable to observe what happens before his entry in the game. Past information is therefore conveyed from one cohort to the next by means of communication.When communication is costless and messages are sent simultaneously, communication mechanisms or protocols exist that sustain the same set of equilibrium payoffs as in the standard repeated game. When communication is costless but sequential, the incentives to whitewash the unobservable past history of play become pervasive. These incentives to whitewash can only be countered if some player serves as a neutral historian who verifies the truthfulness of others reports while remaining indifferent in the process. By contrast, when communication is sequential and (lexicographically) costly, all protocols admit only equilibria that sustain stage Nash equilibrium payoffs.We also analyze a centralized communication protocol in which history leaves a footprint that can only hidden by the current cohort by a unanimous coverup. We show that in this case the set of payoffs that are sustainable in equilibrium coincides with the weakly renegotiation proof payoffs of the standard repeated game.Received: 30 September 2002, Revised: 5 August 2003, JEL Classification Numbers: C72, C73, D82.We wish to thank an Associate Editor and Dino Gerardi as well as seminar participants at Arizona State, Columbia, Duke, Georgetown, Indiana, Montreal, Princeton, Rochester, Vanderbilt, VPI, the 2001 NSF/NBER Decentralization Conference, the Summer 2001 North American Econometric Society Meetings, and the Midwest Theory Conference, 2000, for useful comments and suggestions. All errors are our own.     

Intrinsic and instrumental reciprocity: An experimental study

In the context of an indefinitely repeated veto game, we devise an experiment to distinguish between alternative explanations of generous behavior (accepting negative payoffs): altruism, intrinsic backward-looking reciprocity, and instrumental forward-looking reciprocity. Our results are broadly consistent with the hypothesis that observed sacrifices are motivated by equilibrium selfish, forward-looking reciprocal behavior although we find a more subtle way in which past kindness affects behavior.     

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.     

Peer pressure,social spillovers,and reciprocity: an experimental analysis

This study examines whether reciprocity is affected by what others know and do. Two types of social effects are investigated within the framework of a modified investment game. On the one hand, we assess the role played by the awareness that own choices are observed by another trustee—i.e., peer pressure. On the other hand, we measure the interaction between trustees’ choices—i.e., social spillovers. We find that peer pressure fosters reciprocity and, to a lesser extent, so do social spillovers.     

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.     

Social status and group norms: Indirect reciprocity in a repeated helping experiment

In the economic literature, reciprocity is typically studied in situations of repeated interaction between two individuals. It refers to one individual rewarding kind acts of the other or punishing hostile acts. In contrast, this paper studies indirect reciprocity, where a cooperative action is rewarded by a third actor, not involved in the original exchange. We provide experimental evidence on indirect reciprocity. The experiment is based on the ‘repeated helping game’ developed by Nowak and Sigmund (J. Theoret. Biol. 194 (1998) 561; Nature 393 (1998) 573), involving random pairing in large groups. Pairs consist of a donor and a recipient. Donors decide whether or not to provide costly ‘help’ to the recipients they are matched with, based on information about the recipient's behavior in encounters with third parties. We observe clear evidence of indirect reciprocity. Many decision-makers respond to the information about previous decisions (whether or not to help others) of the recipients. In our experiments, this indirect reciprocity is largely based on norms about how often the recipient should have helped others in the past. We show that these norms develop similarly within groups of interacting subjects, but distinctly across groups. This leads to the emergence of group norms.     

Finitely repeated games with social preferences

A well-known result from the theory of finitely repeated games states that if the stage game has a unique equilibrium, then there is a unique subgame perfect equilibrium in the finitely repeated game in which the equilibrium of the stage game is being played in every period. Here I show that this result does in general not hold anymore if players have social preferences of the form frequently assumed in the recent literature, for example in the inequity aversion models of Fehr and Schmidt (Quartely Journal of Economics 114:817–868, 1999) or Bolton and Ockenfels (American Economic Review 100:166–193, 2000). In fact, repeating the unique stage game equilibrium may not be a subgame perfect equilibrium at all. This finding should have relevance for all experiments with repeated interaction, whether with fixed, random or perfect stranger matching.     

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     

WHY REWARDS ARE BETTER THAN SANCTIONS

Sanctions are said to fail because of the “rally‐round‐the‐flag effect”. This is the main reason why many advocate the use of positive incentives as a viable alternative. Not only do rewards provoke no defensive reaction, but they may elicit a rally in support of compliance – a “fifth‐column effect.” Yet, positive incentives are vulnerable to extortion – doing wrong in the hope of obtaining larger rewards. As a result, many conjecture that sanction threats and promises of reward are most efficient when used simultaneously. We put this conjecture to a test, staging a formal confrontation of the two forms of incentives. Our model pits a sanctioner and a target in a game allowing for the possibility of rally‐round‐the‐flag, fifth‐column, and extortion effects. The game yields unambiguous results: under no circumstances should a sanctioner prefer sanction threats to reward promises. This result holds despite the risk of extortion, a risk that proves to be less of a drawback than the rally round the flag.     

Why are Small Firms Different? Managers’ Views

Do incentives differ between large and small organizations? Results from a representative survey of compensation managers are used to shed light on the issues. I find that (i) small establishments rely less on pecuniary incentives, and have a significantly more hostile attitude towards incentive schemes based on competition and relative rewards; (ii) large units are more vulnerable to mechanisms of efficiency wages, effects that remain even after controlling for differences in monitoring ability; (iii) large units are more prone to indicate that negative reciprocity is important, and that their employees care about relative pay. I argue that these findings fit with behavioral stories of incentives and motivation, in particular those stressing group interaction effects, inequity aversion and gift exchange.