A General Class of Adaptive Strategies
Sergiu Hart and Andreu Mas-Colell
We exhibit and characterize an entire class of simple adaptive
in the repeated play of a game, having the Hannan-consistency
the long-run, the player is guaranteed an average payoff as large
best-reply payoff to the empirical distribution of play of the
players; i.e., there is no "regret." Smooth fictitious play
Levine [1995, J. Econ. Dynam. Control 19, 1065-1090])
(Hart and Mas-Colell [2000, Econometrica 68,
particular cases. The motivation and application of the current
from the study of procedures whose empirical distribution of play
is, in the
long-run, (almost) a correlated equilibrium. For the analysis we
develop a generalization of Blackwell's (1956, Pacific J. Math.
6, 1-8) approachability strategy for games with vector payoffs.
adaptive strategies; approachability; correlated equilibrium;
fictitious play; regret; regret-matching; smooth fictitious play.
Journal of Economic Literature Classification Numbers:
C7, D7, C6.
Journal of Economic Theory 98 (2001), 1, 26-54