A folk theorem for minority games

Discounted and finitely repeated minority games with public signals

“…Notice that this is equivalent to announcing to each player her own reward at each time, but not the reward of the other players. Renault et al (2005) prove that an undiscounted folk theorem holds for this game, and characterize the set of uniform equilibrium payoffs, i.e. they show that any feasible payoff is an equilibrium payoff.…”

“…The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al (2005), who proved a folk theorem. Here we consider a discounted version and a finitely repeated version of the game, and we strengthen our previous result by showing that the set of equilibrium payoffs Hausdorff-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to infinity.…”

“…Renault et al (2005) are the first to consider a minority game from a traditional strategic viewpoint. In their model an odd number of players have to choose simultaneously one of two rooms.…”

“…The paper by Renault et al (2005) is in the tradition of repeated games with imperfect public monitoring. Examples of such games go back to Rubinstein (1979), Rubinstein andYaari (1983), andRadner (1985) with reference to principal-agent models and by Green and Porter (1984) with reference to oligopoly.…”

“…In this paper we consider a discounted version and a finitely repeated version of the minority game studied by Renault et al (2005). We are able to prove that a version of the folk theorem holds also for these games.…”