DP3856 | Prisoners' Other Dilemma

Publication Date

23/04/2003

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Abstract

Collusive agreements and relational contracts are commonly modeled as equilibria of dynamic games with the strategic features of the repeated Prisoner's Dilemma. The pay-offs agents obtain when being ?cheated upon? by other agents play no role in these models. We propose a way to take these pay-offs into account, and find that cooperation as equilibrium of the infinitely repeated discounted Prisoner's Dilemma is often implausible: for a significant subset of the pay-off discount factor parameter space, all cooperation equilibria are strictly risk dominated in the sense of Harsanyi and Selten (1988). We derive an easy-to-calculate critical level for the discount factor below which this happens, also function of pay-offs obtained when others defect, and argue it is a better measure for the ?likelihood? of cooperation than the critical level at which cooperation is supportable in equilibrium. Our results apply to other games sharing the strategic structure of the Prisoner's Dilemma (repeated oligopolies, relational-contracting models, etc.). We illustrate our main result for collusion equilibria in the repeated Cournot duopoly.