Common Certainty of Rationality Revisited

In conventional epistemic analysis of solution concepts in complete information games, complete information is implicitly interpreted to mean common certainty of (i) a mapping from action profiles to outcomes; (ii) players’ (unconditional) preferences over outcomes; and (iii) players’ preferences over outcomes conditional on others’ actions. We characterize a new solution concept—preference-correlated rationalizability—that captures common certainty of (i) and (ii) but not (iii). We show that it is badly behaved, with failures of upper hemicontinuity giving rise to counter-intuitive results. We discuss restrictions that restore well-behaved results.