Purification in the Infinitely-Repeated Prisoners’ Dilemma

V Bhaskar, George Mailath and Stephen Morris

PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania

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 Välimäki (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)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2004-01-14
New Economics Papers: this item is included in nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:pen:papers:04-004

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