A Few Righteous Men: Imperfect Information, Quit-for-Tat, and Critical Mass in the Dynamics of Cooperation

21 Pages Posted: 23 Aug 2002

See all articles by Serge Moresi

Serge Moresi

Charles River Associates (CRA)

Steven C. Salop

Georgetown University Law Center


This paper explores cooperation incentives in the absence of public reputation information, using an infinite-horizon Prisoners' Dilemma model of sequential relationships. We examine a strategy which we call Quit-for-Tat (QFT). In this model, individuals initially are paired randomly. In the equilibrium with identical profit-maximizing individuals, each initially cooperates with some probability. If both cooperate, they form a long-term cooperative relationship until one dies. If one defects, then the victim quits the relationship and both are paired with others. Defection is not public information, but known only to the victim. There are three possible steady-state equilibria, one in which each person defects every period and, under certain conditions, two partial cooperation QFT equilibria. In these QFT equilibria, a fraction of individuals cooperate initially with new partners (or each individual follows a mixed strategy in the initial interaction with a new partner) and then follow a QFT strategy thereafter. Given this basic structure, if there arises a critical mass of ethical or religious families (a moral minority) who never defect in the initial interaction, but follow QFT afterwards, these "righteous" people (and their righteous offspring) induce a cooperation bandwagon and dramatically increase the equilibrium amount of cooperation in society, despite the lack of public reputation information. Moreover, if the discount rate tends to zero, then the required critical mass of the righteous also tends to zero.

Keywords: Prisoners' Dilemma, random matching, imperfect information, altruism, law and economics, behavioral economics

JEL Classification: C72, C73, D82, D64

Suggested Citation

Moresi, Serge and Salop, Steven C., A Few Righteous Men: Imperfect Information, Quit-for-Tat, and Critical Mass in the Dynamics of Cooperation. ECONOMICS FOR AN IMPERFECT WORLD: ESSAYS IN HONOR OF JOSEPH STIGLITZ, 2 vols., Richard Arnott, Bruce Greenwald, Ravi Kanbur, and Barry Nalebuff, Eds., MIT Press, Forthcoming, Available at SSRN: https://ssrn.com/abstract=320802 or http://dx.doi.org/10.2139/ssrn.320802

Serge Moresi (Contact Author)

Charles River Associates (CRA) ( email )

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Steven C. Salop

Georgetown University Law Center ( email )

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