Purification in the Infinitely-Repeated Prisoners' Dilemma

V Bhaskar, George J. Mailath () and Stephen Morris ()

No 1451, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

Abstract: This paper investigates the Harsanyi-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 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 (search for similar items in EconPapers)
Date: 2004-02
View list of references View citations in EconPapers

Downloads: (external link)
http://cowles.econ.yale.edu/P/cd/d14b/d1451.pdf (application/pdf)

Related works:
Working Paper: Purification in the Infinitely Repeated Prisoners' Dilemma (2004)
Working Paper: Purification in the Infinitely Repeated Prisoner's Dilemma (2006)
Working Paper: Purification in the Infinitely-Repeated Prisoners' Dilemma (2004)
Working Paper: Purification in the Infinitely-Repeated Prisoners' Dilemma (2006)
Working Paper: Purification in the Infinitely-Repeated Prisoners’ Dilemma (2004)
Journal Article: Purification in the Infinitely-Repeated Prisoners' Dilemma
This item may be available elsewhere in EconPapers: Search for items with the same title.

Ordering information: This working paper can be ordered from
Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA
The price is None.

Access Statistics for this paper

More papers in Cowles Foundation Discussion Papers from Cowles Foundation, Yale University
Address: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Contact information at EDIRC.
Series data maintained by Glena Ames ().