Purification in the Infinitely-Repeated Prisoners' Dilemma, Second Version

23 Pages Posted: 22 Aug 2007

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: August 20, 2007

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 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 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.

Note: A previous version of this paper can be found at: http://ssrn.com/abstract=489506

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, Second Version (August 20, 2007). PIER Working Paper No. 07-024, Available at SSRN: https://ssrn.com/abstract=1008474 or http://dx.doi.org/10.2139/ssrn.1008474

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
133 South 36th Street
Philadelphia, PA 19104-6297
United States
215-898-7908 (Phone)
215-573-2057 (Fax)

HOME PAGE: http://web.sas.upenn.edu/gmailath/

Research School of Economics, ANU ( email )

HW Arndt Building
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Australia

Stephen Edward Morris

MIT ( email )

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Cambridge, MA 02139-4307
United States

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

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