A folk theorem for minority games

We study a particular case of repeated games with public signals. In the stage game an odd number of players have to choose simultaneously one of two rooms. The players who choose the less crowded room receive a reward of one euro (whence the name “minority game”). Between the stages, only the current majority room is publicly announced. We show that in the infinitely repeated game any feasible payo can be achieved as a uniform equilibrium payo , and as an almost sure equilibrium payo . In particular we construct an inefficient equilibrium where, with probability one, all players choose the same room at almost all stages. This equilibrium is sustained by punishment phases which use, in a unusual way, the pure actions that were played before start of the punishment.(This abstract was borrowed from another version of this item.)