A general class of adaptive strategies

We exhibit and characterize an entire class of simple adaptive strategies. in the repeated play of a game, having the Hannan-consistency properly: in the long-run, the player is guaranteed an average payoff as large as the be st-reply payoff to the empirical distribution of play of the other players: i.e.. there is no "regret" Smooth fictitious play (Fudenberg and Levins [1 995. J. Econ. Dynam. Control 19, 1065-1090]) and regret-matching (Hart and Mas-Colell [2000. Econometrica 68, 1127-1150]) are particular cases. The mo tivation and application of the current paper corns from the study of proce dures whose empirical distribution of play is, in the long run, ( almost) a correlated equilibrium. For the analysis we first develop a generalization of Blackwell's (1956. Pacific J. Math. 6. 1-8) approachability strategy fo r games with Vector payoffs. (C) 2001 Academic Press.