Strict robustness to incomplete information

We study a strict version of the notion of equilibrium robustness by Kajii and Morris (Econometrica 65:1283–1309, 1997) that allows for a larger class of incomplete information perturbations of a given complete information game, where with high probability, players believe that their payoffs are close to (but may be different from) those of the complete information game. We show that a strict monotone potential maximizer of a complete information game is strictly robust if either the game or the associated strict monotone potential is supermodular, and that the converse also holds in all binary-action supermodular games.