Correlated Equilibrium Under Costly Disobedience

Abstract

A recent experimental literature focusing on overcoming coordination problems in strategic games points out to the need for incentivizing players to follow third-party recommendations to coordinate on better outcomes. In this paper, we consider finite normal-form games to strengthen the incentives in the Aumann's (1974) well-known coordination model under correlated equilibrium by introducing a non-negative cost of disobedience for all players. Calling the new solution costly correlated equilibrium (CCE), we show that in any game that is non-trivial, the set of CCE is larger in the presence of even an arbitrarily small cost of disobedience than in its absence if and only if the game has an unpure Nash equilibrium. We also illustrate that there are games in which strictly better social outcomes can be attained, and the value of mediation increases, even with an arbitrarily small increase in the cost level. In addition, we illustrate how our model can be integrated with a voluntary cost-selection game where players non-cooperatively choose their costs of disobedience before mediation occurs. We show that there exist cost-selection games in which setting the cost level at zero is a strictly dominated strategy for each player as well as games this strategy becomes weakly dominant for everyone.