CONSISTENCY AND CAUTIOUS FICTITIOUS PLAY

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