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Purification in the infinitely-repeated prisoners' dilemma

Bhaskar, V.; Mailath, G.J.; Morris, S.; (2008) Purification in the infinitely-repeated prisoners' dilemma. Review of Economic Dynamics , 11 (3) pp. 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 Välimäki [Ely, J.C., Välimäki, 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.

Type: Article
Title: Purification in the infinitely-repeated prisoners' dilemma
DOI: 10.1016/j.red.2007.10.004
Publisher version: http://dx.doi.org/10.1016/j.red.2007.10.004
Language: English
Additional information: Please see http://eprints.ucl.ac.uk/14515/ for a Working Paper version
Keywords: JEL classification: C72, C73. Purification, belief-free equilibria, repeated games
UCL classification: UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of SandHS > Dept of Economics
URI: http://discovery.ucl.ac.uk/id/eprint/15426
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