Epistemic Robustness Of Sets Closed Under Rational Behavior

This paper provides two conditions of epistemic robustness, robustness to alternative best replies and robustness to non-best replies, and uses these to characterize variants of CURB sets in finite games, including the set of rationalizable strategies. A CURB set - mnemonic for 'Closed Under Rational Behavior' - is a Cartesian product of pure-strategy sets, one for each player, that includes all best replies to all probability distributions over the strategies in the set. Hence, if a player believes that her opponents stick to strategies from their components of a CURB set, then her component contains all her best replies, so she'd better stick to her strategies as well.