Admissibility and Common Knowledge

The implications of assuming that it is commonly known that players consider only admissible best responses are investigated.Within a states-of-the-world model where a state, for each player, determines a strategy set rather than a strategy the concept of fully permissible sets is defined.General existence is established, and a finite algorithm (eliminating strategy sets instead of strategies) is provided.The concept refines rationalizability as well as the Dekel-Fudenberg procedure, and captures a notion of forward induction.When players consider all best responses, the same framework can be used to define the concept of rationalizable sets, which characterizes rationalizability.