Neighborhood stability in sender-receiver games

This paper characterizes robust outcomes in sender-receiver games. An equilibrium (a retract) is perturbed message persistent (PMP) if it is the limit (Hausdorff limit) of persistent equilibria(persistent retracts) in perturbed games. In strict common interestgames separating equilibria are PMP and message invariant equilibria are not PMP. With partial common interest, there exists a PMP retract which partially separates types and message invariant equilibria are not PMP. Under a rich language condition only partially separating equilibria are PMP in partial common interest games, and there are further results on refinements and games where the sender has a preferred equilibrium. Journal of Economic Literature Classification Numbers: C72, D82.