Prisoners' other Dilemma

We ...nd that cooperation as equilibrium of the in...nitely repeated discounted Prisoner’s Dilemma is often not plausible: For a signi...cant subset of the payo¤discount factor parameter space, all co-operation equilibria are strictly risk dominated (in the sense of Harsanyi and Selten, 1988) by defection. We derive an easy-to-calculate critical level for the discount factor ±¤ below which this happens, and argue it is a better measure for the “likelihood” of cooperation than the critical level ± < ±¤ at which cooperation is supportable in equilibrium. Su¢cient conditions are provided for cooperation equilibria to be risk perfect, i.e. not to be risk dominated at any subgame. Our results apply to other games sharing the strategic structure of the repeated Prisoner’s Dilemma (repeated oligopolies, relational-contracting models, etc.). We illustrate our main result for collusion equilibria in the repeated Cournot duopoly. JEL Classi...cation Numbers: C72, L13, L14, M50. ¤We appreciate suggestions and remarks by Geir Asheim, Eric van Damme, Christian Ewerhart, David Levine, Georg Nöldeke, Reinhard Selten and various seminar participants in Berkeley, Bonn, Frankfurt, Mannheim, Stanford, Stockholm, Tilburg, and Zürich. This project has been supported by grants from the DFG (BL418/4-1) for Blonski, and from the European Commission (EGEMTPS/RTN) for Spagnolo. yDepartment of Economics, Goethe University, Frankfurt am Main, 60054 Frankfurt a.M., Germany; telephone: +49-(0)69-798-23858; e-Mail: [email protected] zDepartment of Economics, University of Mannheim, and C.E.P.R. e-Mail: [email protected]