Prisoners' Other Dilemma
J.W.Goethe University, Frankfurt, Economics Working Paper
24 Pages Posted: 9 Aug 2001 Last revised: 1 Oct 2008
Date Written: December 2004
We find that - contrary to common perception - co-operation as equilibrium of the infinitely repeated discounted Prisoner's Dilemma is in many relevant cases not very plausible: For a significant subset of the payoff-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 co-operation than the critical level at which co-operation is supportable in equilibrium. The results apply to other games sharing the strategic features of the repeated Prisoner's Dilemma, such as models of implicit/relational contracts, common pools and public good provision. We illustrate our main result for collusion equilibria in the repeated Cournot duopoly.
Keywords: Risk Dominance, repeated games, Prisoner's Dilemma, relational contracts
JEL Classification: C73
Suggested Citation: Suggested Citation