Private-Beliefs Equilibrium

Ehud Kalai and Ehud Lehrer ()

No 926, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

Abstract: At a private-beliefs equilibrium of an n-person infinitely repeated game with discounting, each player maximizes his expected payoff relative to some private, possibly false, belief regarding the strategies chosen by his opponents. Moreover, the probability distribution induced over the observed play paths of the game according to his belie coincides with the one actually played. Thus, any statistical updating can only reinforce the beliefs. It is shown that if the game is played with perfect monitoring, then the joint behavior induced by a private-beliefs equilibrium coincides with a behavior induced by a Nash equilibrium even when perturbations are allowed.

Date: 1991-01
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Working Paper: Private-Beliefs Equilibrium (1991)
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