Rationalizability and epistemic priority orderings
At the beginning of a dynamic game, players may have exogenous theories about how the opponents will play. If these theories are commonly known, players will refine their first-order beliefs and challenge their own theories through strategic reasoning. I propose a new solution concept, Selective Rationalizability, which captures the following hypothesis: when the observed behavior is not compatible with the beliefs in rationality and in the theories of all orders, players keep the beliefs in rationality that are compatible with the observed behavior, and drop the incompatible beliefs in the theories. Thus, Selective Rationalizability captures Common Strong Belief in Rationality (Battigalli and Siniscalchi, 2002) and refines Extensive-Form Rationalizability (Pearce, 1984, Battigalli, 1996), whereas Strong-Δ-Rationalizability (Battigalli, 2003, Battigalli and Siniscalchi, 2003) captures the opposite epistemic priority choice. Selective Rationalizability is extended to encompass richer epistemic priority orderings among different theories of opponents' behavior. This allows to shed some new light on strategic stability (Kohlberg and Mertens, 1986).