An Example
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The Battle of the sexes, as shown, is a two player coordination game. Both Opera/Opera and Football/Football are Nash equilibria. Any probability distribution over these two Nash equilibria is a correlated equilibrium. The question then becomes which of the infinitely many possible equilibria should be chosen by the two players. If they disagree and choose different distributions, they are likely to receive 0 payoffs. In this symmetric case the natural choice is to play Opera/Opera and Football/Football with equal probability. Indeed all bargaining solutions described below prescribe this solution. However, if the game is asymmetric --- for example, Football/Football instead yields payoffs of 2,5 --- the appropriate distribution is less clear. The problem of finding such a distribution is addressed by the bargaining theory.
Read more about this topic: Bargaining Problem
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