Purification in the Infinitely-Repeated Prisoners’ Dilemma

V Bhaskar, George Mailath and Stephen Morris

Economics Discussion Papers from University of Essex, Department of Economics

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 a class of one-period memory mixed strategy equilibria used by Ely and V¨alim¨aki (2002) in their study of the repeated prisoners’ dilemma with private monitoring. We find that the strategy profile is purifiable by perturbed-game finite-memory strategies if and only if it is strongly symmetric, in the sense that after every history, both players play the same mixed action. Thus “most” strategy profiles are not purifiable by finite memory strategies. However, if we allow infinite memory strategies in the perturbed game, then any completely-mixed equilibrium is purifiable.

Keywords: Purification; repeated games; belief-free equilibria; imperfect monitoring. (search for similar items in EconPapers)
Date: 2004
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Related works:
Journal Article: Purification in the Infinitely-Repeated Prisoners' Dilemma (2008)
Working Paper: Purification in the Infinitely-Repeated Prisoners' Dilemma (2007)
Working Paper: Purification in the Infinitely Repeated Prisoner's Dilemma (2006)
Working Paper: Purification in the Infinitely-Repeated Prisoners' Dilemma (2006)
Working Paper: Purification in the Infinitely Repeated Prisoners' Dilemma (2004)
Working Paper: Purification in the Infinitely-Repeated Prisoners' Dilemma (2004)
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