Title: Rationalizability and Epistemic Priority Orderings,
Abstract: At the beginning of a dynamic game, players may have exogenous theories about
how the opponents are going to play. Suppose that these theories are commonly
known. Then, players will refine their first-order beliefs, and challenge their
own theories, through strategic reasoning. I develop and characterize
epistemically a new solution concept, Selective Rationalizability, which
accomplishes this task under the following assumption: when the observed
behavior is not compatible with the beliefs in players' rationality and
theories of all orders, players keep the orders of belief in rationality that
are per se 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; BS, 2002), whereas
Strong-$\Delta$-Rationalizability (Battigalli, 2003; Battigalli and
Siniscalchi, 2003) captures the opposite epistemic priority choice. Selective
Rationalizability can be extended to encompass richer epistemic priority
orderings among different theories of opponents' behavior. This allows to
establish a surprising connection with strategic stability (Kohlberg and
Mertens, 1986).