A note on rationalizability and restrictions on belief

Rationalizability is a widely accepted solution concept in the study of strategic form game with complete information and is fully characterized in terms of assumptions on the rationality of the players and common certainty of rationality. Battigalli and Siniscalchi extend rationalizability and derive the solution concept called ?-rationalizability. Their analysis is based on the following assumptions: (a) players are rational; (b) their first-order beliefs satisfy some restrictions; and (c) there is common belief of (a) and (b). In this note I focus on games with complete information and I characterize ?-rationalizability with a new notion of iterative dominance which is able to capture the additional hypothesis on players' beliefs.