The robust selection of rationalizability

We propose a notion of selecting rationalizable actions by perturbing players' higher-order beliefs, which we call robust selection. Similarly to WY selection [28], robust selection generalizes the idea behind the equilibrium selection in the email game [27] and the global game [3]. In contrast to WY selection, however, we require selection to be robust to misspecifications of payoffs. Robust selection is a strong notion in the sense that, among types with multiple rationalizable actions, “almost all” selections are fragile; but it is also a weak notion in the sense that any strictly rationalizable action can be robustly selected. We show that robust selection is fully characterized by the curb collection, a notion that generalizes the curb set in [2]. We also use the curb collection to characterize critical types [12] in any fixed finite game.