Purification in the Infinitely-Repeated Prisoners' Dilemma

18 Pages Posted: 20 Jul 2006

See all articles by V. Bhaskar

V. Bhaskar

University College London

George J. Mailath

University of Pennsylvania - Department of Economics; Research School of Economics, ANU

Stephen Morris

MIT

Date Written: July 2006

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 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.

Keywords: Purification, Belief-free equilibria, Repeated games

JEL Classification: C72, C73

Suggested Citation

Bhaskar, V. and Mailath, George J. and Morris, Stephen Edward, Purification in the Infinitely-Repeated Prisoners' Dilemma (July 2006). Cowles Foundation Discussion Paper No. 1571, Available at SSRN: https://ssrn.com/abstract=917908

V. Bhaskar

University College London ( email )

Gower Street
London
United Kingdom

George J. Mailath (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
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Philadelphia, PA 19104-6297
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HOME PAGE: http://web.sas.upenn.edu/gmailath/

Research School of Economics, ANU ( email )

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Stephen Edward Morris

MIT ( email )

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HOME PAGE: http://https://economics.mit.edu/faculty/semorris

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