A Theory of Sequential Reciprocity

Many experimental studies indicate that people are motivated by reciprocity. Rabin (1993) develops techniques for incorporating such concerns into game theory and economics. His model, however, does not fare well when applied to situations with an interesting dynamic structure (like many experimental games), because it is developed for normal form games in which information about the sequential structure of a strategic situation is suppressed. In this paper we develop a theory of reciprocity for extensive games in which the sequential structure of a strategic situation is made explicit. We propose a new solution concept— sequential reciprocity equilibrium—which is applicable to extensive games, and we prove a general equilibrium existence result. The model is applied in several examples, including some well known experimental games like the Ultimatum game and the Sequential Prisoners’ Dilemma.Reciprocity;extensive games

Sequential reciprocity in two-player, two-stage games: An experimental analysis.

We experimentally test Dufwenberg and Kirchsteiger’s (2004) theory of sequential reciprocity in a sequential prisoner’s dilemma (SPD) and a mini-ultimatum game (MUG). Data on behavior and first- and second-order beliefs allow us to classify each subject’s behavior as a material best response, a reciprocity best response, both, or none. We found that in both games the behavior of about 80% of the firstmovers was a material best response, a reciprocity best response, or both. The remaining 20% of first-movers almost always made choices that were “too kind” according to the theory of reciprocity. Secondmover behavior, in both games, was fully in line with the predictions of the theory. The average behavior and beliefs across subjects were compatible with a sequential reciprocity equilibrium in the SPD but not in the MUG. We also found first- and second-order beliefs to be unbiased in the SPD and nearly unbiased in the MUG.Sequential reciprocity; Sequential prisoner’s dilemma; Mini-ultimatum game;

Perfect Sequential Reciprocity and Dynamic Consistency

Dufwenberg and Kirchsteiger�s (2004) extends Rabin�s (1993) theory of reciprocity in a dynamic sense, introducing a rule of revision for player�s beliefs. The Sequential Reciprocity Equilibrium [SRE] they define can be dynamically inconsistent. In this article it is argued that such dynamic inconsistency is not intrinsically related to issues of reciprocity, but rather to the particular way the beliefs�updating process is modeled. A refinement of the SRE, which is both dynamically consistent and, it is argued, more sound to assumptions usually made in the literature of information economics and philosophy, is proposed.Reciprocity;� Dynamic Consistency

A Theory of Sequential Group Reciprocity

Games that appear to be independent, involving none of the same players, may be related by emotions of reciprocity between the members of the same groups. In the real world, individuals are members of groups and want to reward or punish those groups whose members have been kind or unkind to members of their own. In this paper we extend Dufwenberg and Kirchsteiger's model of sequential reciprocity (2004) to groups of individuals and define a new "sequential group reciprocity equilibrium" for which we prove its existence. We study the case of two games with two players in each game, where each player belongs to the same group as a player in the other game. We show that when the payoffs of one game are much higher than the payoffs of the other, the outcome of the game with higher payoffs determines the outcome of the other game. We also find that when the payoffs are very asymmetric, the outcome where the sum of the payoffs is maximized is a sequential group reciprocity equilibrium

The impact of relative position and returns on sacrifice and reciprocity: an experimental study using individual decisions

We present a comprehensive experimental design that makes it possible to characterize other-regarding preferences and their relationship to the decision maker’s relative position. Participants are faced with a large number of decisions involving variations in the trade-offs between own and other’s payoffs, as well as in other potentially important factors like the decision maker’s relative position. We find that: (1) choices are responsive to the cost of helping and hurting others; (2) The weight a decision maker places on others’ monetary payoffs depends on whether the decision maker is in an advantageous or disadvantageous relative position; and (3) We find no evidence of reciprocity of the type linked to menu-dependence. The results of a mixture-model estimation show considerable heterogeneity in subjects’ motivations and confirm the absence of reciprocal motives. Pure selfish behavior is the most frequently observed behavior. Among the subjects exhibiting social preferences, social-welfare maximization is the most frequent, followed by inequality-aversion and by competitiveness

Information seeking and reciprocity: A transformational analysis

The motivation to reciprocate is analyzed within the framework of interdependence theory, with focus on the process of transformation of situations. A model of transformation is presented for the motivation to reciprocate and hypotheses regarding allocation behavior and information seeking are derived. The hypotheses are tested in two experiments implementing a game where participants allocate payoff to self and other in a sequential way, with one participant able to gather costly information regarding the other's previous behavior. Individual differences in the motivation to reciprocate are assessed with the Personal Norm of Reciprocity questionnaire. Results show that participants with high motivation to reciprocate seek information regarding other's past behavior, and react to this information as the norm of reciprocity prescribes. Participants with low motivation to reciprocate prefer information regarding the future of the interaction (Study 1), or no information (Study 2), and behave in a more selfish way. Results are discussed with respect of (1) the transformation of situation process, (2) the role of reciprocity as an interpersonal motive, and (3) the validity of the individual differences measure. Copyright © 2003 John Wiley & Sons, Ltd

Intention-based economic theories of reciprocity

Recientemente, varios experimentos han mostrado que los individuos exhiben un comportamiento auténticamente recíproco en interacciones anónimas que se dan una sola vez ('one-shot'). En tanto que se ha mostrado que la reciprocidad es relevante en múltiples campos de la economía, han existido varios intentos por modelar el comportamiento recíproco. Este documento revisa los modelos de reciprocidad que se fundamentan en las intenciones y presenta un ejemplo para el caso del manejo de los profesores en el sector público, en el que el gobierno ofrece un esquema de incentivos para la implementación de un programa. Este esquema tiene la estructura del dilema del prisionero. Tanto en los juegos simultáneos como secuenciales, los resultados de equilibrio puede ser distintos a los que predice la teoría convencional. ************************************************************************ In recent years, several experiments have shown that individuals exhibit authentic reciprocal behavior in anonymous one-shot interactions. As reciprocity has been shown to be relevant in several economic fields, there have also been several attempts to model reciprocical behavior. I review the intention-based models of reciprocity and present an example in teachers´ management in the public sector in which a government offers an incentive scheme to implement a program. The incentive scheme has the prisioner’s dilemma structure, In both simultaneous and sequential games, in equilibrium reciprocal teachers may reach other equilibria different from those predicted by the standard theory.Game theory, psychological games,Intention-based models, reciprocl behaviour