A General Class of Adaptive Strategies

Sergiu Hart & Andreu Mas-Colell

We exhibit and characterize an entire class of simple adaptive strategies,in the repeated play of a game, having the Hannan-consistency property: In the long-run, the player is guaranteed an average payoff as large as the best- reply payoff to the empirical distribution of play of the other players; i.e., there is no "regret." Smooth fictitious play (Fudenberg and Levine [19951) and regret-matching (Hart and Mas-Colell [1998]) are particular cases. The motivation and application of this work come from the study of procedures whose empirical distribution of play is, in the long-run, (almost) a correlated equilibrium. The basic tool for the analysis is a generalization of Blackwell's [1956a) approachability strategy for games with vector payoffs. Keywords: adaptive strategies, approachability, correlated equilibrium, fictitious play, regret. Journal of Economic Literature Classification: C7, D7, C6

March, 1999
Published in: 
Journal of Economic Theory 98(2001), 26-54