On the robustness of equilibrium refinements

The philosophy of equilibrium refinements is that the analyst, if he knows things about the structure of the game, can reject some Nash equilibria as unreasonable. The word “know” in the preceding sentence deserves special emphasis. If in a fixed game the analyst can reject a particular equilibrium outcome, but he cannot do so for games arbitrarily “close by,” then he may have second thoughts about rejecting the outcome. We consider several notions of distance between games, and we characterize their implications for the robustness of equilibrium refinements.