Document Type
Discussion Paper
Publication Date
2-1-2004
CFDP Number
1451
CFDP Pages
19
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 Välimäki 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.
Recommended Citation
Bhaskar, V.; Mailath, George J.; and Morris, Stephen, "Purification in the Infinitely-Repeated Prisoners’ Dilemma" (2004). Cowles Foundation Discussion Papers. 1727.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/1727