A Theory of Sequential Group Reciprocity

Moreno-Okuno, Alejandro T. and Mosiño, Alejandro (2017): A Theory of Sequential Group Reciprocity.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Fairness, Groups, Psychological Games, Game Theory
• Subjects: A - General Economics and Teaching > A1 - General Economics > A12 - Relation of Economics to Other Disciplines; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General; D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

References

Abbink, K. & Herrmann, B. (2009). Pointless Vendettas. Centre for Behavioral and Experimental Social Science Discussion Paper 09-10.

Akerlof, G.A. & Kranton, R.E. (2000). Economics and Identity. The Quarterly Journal of Economics 115(3), 715-753.

Ayres, I. & Siegelman P. (1995). Race and Gender Discrimination in Bargaining for a New Car. The American Economic Review 85(3), 304-321.

Bolton G.E. & Ockenfels A. (2000). ERC: A Theory of Equity, Reciprocity, and Competition. American Economic Review 90(1), 166-193.

Chen Y. & Li S.X. (2009). Group Identity and Social Preferences. The American Economic Review 99(1), 431-457.

Dufwenberg, M. & Kirchsteiger, G. (2004). A Theory of Sequential Reciprocity, Games and Economic Behavior 47(2), 268-298.

Edwards R., Gut A. & Mavondo F., 2007. Buyer animosity in business to business markets: Evidence from the French nuclear tests. Industrial Marketing Management 36(4), 483-492.

Engelmann D. & Fischbacher U. (2008). Indirect reciprocity and strategic reputation building in an experiment helping game. Games and Economic Behavior 67(2), 399--407.

Falk A. & Fischbacher U. (2006). A theory of reciprocity. Games and Economic Behavior 54(2), 293-315.

Fearon J.D. & Laitin D.D. (1996). Explaining Interethnic Cooperation. The American Political Science Review 90(4), 715-735.

Fehr E. & Schmidt K. (1999). A Theory of Fairness, Competition, and Cooperation. The Quarterly Journal of Economics 114(3), 817-868.

Fehr E. & Fischbacher U. (2004). Third-party punishment and social norms. Evolution and Human Behavior 25(2), 63-87.

Geanakoplos J., Pearce D. & Stacchetti E. (1989). Psychological games and sequential rationality, Games and Economic Behavior 1(1), 60-79.

Goette, L., Huffman, D. & Meier, S. (2006). The Impact of Group Membership on Cooperation and Norm Enforcement: Evidence Using Random Assignment to Real Social Groups. The American Economic Review, 96(2), 212-216.

Huck S. & Lünser G. (2010). Group reputations. An experiment foray. Journal of Economic Behavior and Organization 73(2), 153-157.

Hugh-Jones, D. & Leroch, M.A. (2010). Group Reciprocity. Jena Economic Research Papers 2010 - 066.

Janis I.L. (1963). Group identification under conditions of external danger, British Journal of Medical Psycholy 36(3), 227--238.

Levine, D.K. (1998). Modeling Altruism and Spitefulness in Experiments. Review of Economic Dynamics 1(3), 593-622.

Lundsgaarde E., Breunig C., & Prakash A. (2010). Instrumental Philanthropy: Trade and the Geographical Distribution of Foreign Aid. Canadian Journal of Political Science 43(3), 733--761.

Michaels, G. & Zhi, X. (2010). American Economic Journal: Applied Economics 2(3), 256-281.

Mitchell, T.L., Haw R.M., Pfeifer J.E. & Meissner, C.A. (2005). Racial Bias in Mock Juror Decision-Making: A Meta-Analytic Review of Defendant Treatment. Law and Human Behavior 29(6), 621-637.

Nowak, M.A. & Sigmund, K. (1998). Evolution of indirect reciprocity by image scoring, Nature 393, 573-577.

Nowak, M.A. & Sigmund, K. (2005). Evolution of indirect reciprocity, Nature 437, 1291-1298.

Price, J. & Wolfers, J. (2010). Racial Discrimination among NBA Referees. The Quarterly Journal of Economics 125(4), 1859-1887.

Rabin M. (1993). Incorporating Fairness into Game Theory and Economics. The American Economic Review 83(5), 1281-1302.

Shayo, M. & Zussman, A. (2011). Judicial Ingroup Bias in the Shadow of Terrorism. The Quarterly Journal of Economics 126(3), 1447-1484.

Tajfel H., Billig, M.G., Bundy, R.P. & Flament C. (1971). Social categorization and intergroup behaviour. European Journal of Social Psychology 1(2), 149-178.

Tirole J., (1996). A Theory of Collective Reputations (with applications to the persistence of corruption and to firm quality). The Review of Economic Studies 63, 1-22.

Zussman, A. (2013). Ethnic discrimination: lessons from the israeli online market for used cars, The Economic Journal, doi: 10.1111/ecoj.12059