On the Epistemic Foundation for Iterated Weak Dominance: An Analysis in a Logic of Individual and Collective attitudes

Given certain assumptions about the agents (e.g., rationality), under which conditions will they play what the solution concept prescribes? Are these conditions irrealistic? Are they too strong for the domain of application under consideration? 2 Interactive epistemology Analysis of the (necessary and/or sufficient) epistemic conditions of equilibrium notions. E.g.: logical omniscience common belief about rationality of every player knowledge about other players' choices (i.e., if a given player i chooses the action a, then every player knows this) ... α β α β If Row is rational then his only reason for discarding B is that he envisages the possibility that Column will play β α β α β If Column is rational then her reason for discarding β is that she considers the situation in which Row plays (the admissible strategy) A strictly more plausible than the situation in which Row plays (the inadmissible strategy) C ⇒ Second requirement for IDWDS: according to a given player, situations in which other players play rationally are strictly more plausible than situations in which they play irrationally 6 α β α β If Column is rational then her reason for discarding β is that she considers the situation in which Row plays (the admissible strategy) A strictly more plausible than the situation in which Row plays (the inadmissible strategy) C ⇒ Second requirement for IDWDS: according to a given player, situations in which other players play rationally are strictly more plausible than situations in which they play irrationally This entails some kind of belief robustness: the player will continue to believe that others will play rationally as long as he does not learn something which is incompatible with this fact 6 Motivation