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

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