Common assumption of cautious rationality and iterated admissibility

Iterated admissibility, i.e. the iterated deletion of weakly dom- inated strategies, is an important and extensively applied solution concept for complete information games. To understand when it is the appropriate one, conditions under which players want to avoid strategies that are weakly dom- inated in some reduced game along the procedure (although possibly not in the …nal set!) must be provided. It is intuitive that these conditions have to incorporate some cautious attitude of the players. Yet, to what extent players are cautious and assume that opponents are must be carefully de…ned in or- der to provide a correct motivation for iterated admissibility. Brandenburger, Friedenberg and Keisler (ECMA, 2008) de…ne a notion of rationality, including a full-support requirement for lexicographic beliefs, which delivers iterated ad- missibility when players adopt it, assume (to a de…ned extent) that opponents adopt it, and so on, up to some …nite level. This notion of rationality cannot be commonly assumed in their sense by players unless heavy exogenous re- strictions to beliefs apply. Here, we provide meaningful but weaker notions of cautiousness and assumption such that cautious rationality can be commonly assumed by players and iterated admissibility is captured.