Purification in the Infinitely-Repeated Prisoners' Dilemma
18 Pages Posted: 20 Jul 2006
Date Written: July 2006
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 a class of one-period memory mixed strategy equilibria used by Ely and Valimaki (2002) in their study of the repeated prisoners' dilemma with private monitoring. We find that all such strategy profiles are 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.
Keywords: Purification, Belief-free equilibria, Repeated games
JEL Classification: C72, C73
Suggested Citation: Suggested Citation