Purification in the infinitely-repeated prisoners' dilemma

V. Bhaskar, George J. Mailath, Stephen Morris

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24 Scopus citations


This paper investigates the Harsanyi [Harsanyi, J.C., 1973. Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points. International Journal of Game Theory 2 (1), 1-23]-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 [Ely, J.C., Välimäki, J., 2002. A robust folk theorem for the prisoner's dilemma. Journal of Economic Theory 102 (1), 84-105] 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.

Original languageEnglish (US)
Pages (from-to)515-528
Number of pages14
JournalReview of Economic Dynamics
Issue number3
StatePublished - Jul 2008

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics


  • Belief-free equilibria
  • Purification
  • Repeated games


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