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Unité Mixte de Recherche du C.N.R.S. N°7534
Abstract : We consider a repeated game where at each stage players simultaneously choose one of two rooms. The players who choose the less crowded room are rewarded with one euro. 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 the authors, who proved a folk theorem (2005). 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 diverges to infinity. We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria. We consider a variation of the minority game with an extra player, and we prove that private strategies allow to achieve in equilibrium some Pareto-efficient payoffs that public strategies cannot achieve.
Discounted and Finitely Repeated Minority Games with Public Signals
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