A Notion of Consistent Rationalizability - Between Weak and Pearce's Extensive Form Rationalizability

Ben-Porath (1997) characterizes the strategies consistent with common certainty of rationality (CCR) and the origin of a generic game of perfect information. More generally, the notion of "weak extensive form rationalizability" (weak EFR) captures the implications initial CCR in an extensive form game. We go one step further by ascertaining at which additional information sets initial CCR can be maintained "consistently". Our consistency notion has two aspects: we examine whether there is "internal consistency" in assuming CCR at a given collection of information sets by using Battigalli and Siniscalchi's (1999) recent result while we introduce "external consistency" to account for all reachable information sets. For a class of games, including all belief- consistent games [cf. Reny (1993)], we identify a unique collection of information sets and hence a unique set of strategy profiles; moreover, we show that in this case our notion is outcome-equivalent to Pearce's (1984) EFR. But in general out notion is between weak and Pearce's EFR.