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 (Weinstein and Yildiz 2007), robust selection generalizes the idea behind the equilibrium selection in the email game (Rubinstein 1989) and the global game (Carlsson and Van Damme 1993). 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 (Basu and Weibull 1991). We also use the curb collection to characterize critical types (Ely and Peski 2011) in any fixed finite game.