Communication-proof equilibria in cheap-talk games

We define communication-proof equilibria in simple games of communication. These equilibria satisfy a stability condition guaranteeing that they would not be affected if new opportunities to communicate arose. We look for partitions of possible equilibria into sets of good and bad equilibria. The good equilibria are those that cannot be destabilized by another good equilibrium. The remaining equilibria are bad. An equilibrium for the original game is communication proof if its is a good equilibrium in a partition of this form. We prove that communication-proof equilibria exist and, for a class of common-interest games, communication-proof outcomes are efficient. Journal of Economic Literature Classification Numbers: C72, D80.