To “ Admissibility in Games ” : Appendices

Section S.1 continues the discussion in the main text of the definition of assumption and of the relationship between assumption and the concepts of (i) infinitely more likely than (Blume, Brandenburger, and Dekel (1991), henceforth BBD) and (ii) strong belief (Battigalli and Siniscalchi (2002), henceforth B-S). The focus is on the behavior of the assumption concept in the game, theoretic setting. Section S.2 examines our negative result (Theorem 10.1). It is impossible (under certain conditions) for rationality and common assumption of rationality (RCAR) to hold in a complete structure based on lexicographic probability systems (our Theorem 10.1). But it is possible for rationality and common strong belief of rationality (RCSBR) to hold in a complete structure based on conditional probability systems (Proposition 6 in B-S). What accounts for the difference? Finally, Section S.3 expands on the coverage of the literature in the main text.