Purification in the Infinitely-Repeated Prisoners’ Dilemma
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.
Bhaskar, V.; Mailath, George J.; and Morris, Stephen, "Purification in the Infinitely-Repeated Prisoners’ Dilemma" (2006). Cowles Foundation Discussion Papers. 1862.