Plenary talk: 1994 Society for Economic Dynamics and Control Meetings, Journal of Economic Dynamics and Control, 19 (1995) 1065-1090.

Full Text

Consistency and Cautious Fictitious Play

Drew Fudenberg and David K. Levine

June 10, 1994

Revised: November 29, 1996

Abstract: We study a variation of fictitious play, in which the probability of each action is an exponential function of that action's utility against the historical frequency of opponents' play. Regardless of the opponents' strategies, the utility received by an agent using this rule is nearly the best that could be achieved against the historical frequency. Such rules are approximately optimal in i.i.d. environments, and guarantee nearly the minmax regardless of opponents' behavior. Fictitious play shares these properties provided it switches "infrequently" between actions. We also study the long run outcomes when all players use consistent and cautious rules.