Hierarchies of conditional beliefs and interactive epistemology in dynamicgames

The epistemic analysis of solution concepts for dynamic games involves stat ements about the players' beliefs conditional upon different histories of p lay, their conditional beliefs about each other's conditional beliefs, etc. To represent such statements, we construct a space of infinite (coherent) hierarchies of conditional probability systems, defined with respect to ii fixed collection of. relevant hypotheses concerning an external state (e.g. , the strategy profile being played.) As an application, we derive results about common certainly of the opponent's rationality conditonal on an arbit rary collection of histories in multistage games with observed actions and (possibly) incomplete information. Classification Numbers: C72, D82. (C) 19 99 Academic Press.