Correlated Polyequilibrium

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Polyequilibrium is a set-valued generalization of Nash equilibrium that differs in specifying strategies that players do not choose, such that for each excluded strategy of each player there is a non-excluded strategy that responds at least as well as the first one does to every profile of non-excluded strategies. This paper introduces a corresponding generalization of correlated equilibrium, correlated polyequilibrium, which is defined as a polyequilibrium in an “augmented” game where players choose their action only after receiving random private signals from some correlation device, or mechanism. The players’ choices yield a set of distributions of strategy profiles, which may not include any correlated equilibrium distribution. Correspondingly, some results that do not hold in any correlated equilibrium are obtained in a correlated polyequilibrium.