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Purification in the infinitely-repeated prisoners' dilemma

Bhaskar, V; Mailath, GJ; Morris, S; (2008) Purification in the infinitely-repeated prisoners' dilemma. REV ECON DYNAM , 11 (3) 515 - 528. 10.1016/j.red.2007.10.004.

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Abstract

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 Valimaki [Ely, J.C., Valimaki, 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. (C) 2007 Elsevier Inc. All rights reserved.

Type: Article
Title: Purification in the infinitely-repeated prisoners' dilemma
DOI: 10.1016/j.red.2007.10.004
Keywords: purification, belief-free equilibria, repeated games, REPEATED GAMES, EQUILIBRIA, EFFICIENCY, THEOREM, FOLK
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of SandHS > Dept of Economics
URI: http://discovery.ucl.ac.uk/id/eprint/80926
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