Coordination and Cheap Talk in a Battle of the Sexes
We consider a Battle of the Sexes game with incomplete information and allow cheap talk regarding players' private information before the game is played. We prove that the unique fully revealing symmetric cheap talk equilibrium has a desirable coordination property. Such coordination can also be obtained as a partially revealing cheap talk equilibrium. These outcomes can also be achieved using corresponding incentive compatible mechanisms, however, for different ranges of the prior probability.
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