Purification in the Infinitely-Repeated Prisoners' Dilemma, Second Version

Abstract:     
This paper investigates the Harsanyi (1973)-purifiability of mixed strategies in the repeated prisoners' dilemma with perfect monitoring. We perturb the game so that in each period, a player receives a private payoff shock which is independently and identically distributed across players and periods. We focus on the purifiability of one-period memory mixed strategy equilibria used by Ely and Välimäki (2002) in their study of the repeated prisoners' dilemma with private monitoring. We find that any such strategy profile is not the limit of one-period memory equilibrium strategy profiles of the perturbed game, for almost all noise distributions. However, if we allow infinite memory strategies in the perturbed game, then any completely-mixed equilibrium is purifiable.

Note: A previous version of this paper can be found at: http://ssrn.com/abstract=489506

Keywords: Purification, belief-free equilibria, repeated games

JEL Classifications: C72, C73

Working Paper Series