Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games

Pierpaolo Battigalli, Marciano Siniscalchi
<span title="">1999</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sj24t22gfnfprddmjorsfd6flq" style="color: black;">Journal of Economic Theory</a> </i> &nbsp;
A bstract The epistemic analysis of solution concepts for dynamic games involves statements about the players' beliefs conditional upon dif ferent histories of play, their conditional beliefs about each other's conditional beliefs, etc. We construct a space of infinite (coher ent) hierarchies of conditional probability systems, defined with respect to a fixed collection of relevant hypotheses concerning an external state (e.g. the strategy profile being played). Any (co herent) statement
more &raquo; ... ing the players' dispositions to hold in teractive beliefs has a representation in our "universal" space. As an application, we derive results about common certainty of the opponent's rationality conditonal on an arbitrary collection of his tories in multistage games with observed actions and (possibly) incomplete information. "This paper expands on previous work independently conducted by Pierpaolo Battigalli and Marciano Siniscalchi. We thank the Associate Editor and two anonymous referees for helpful comments. The usual disclaimer applies. Email: battigalffldatacomm. i u e . i t , m arcianoAprineeton. edu. In this paper, we extend this type of construction by considering a space whose elements axe sequences of collections of (conditional) prob abilities. In particular, we consider collections which satisfy Bayes' rule whenever possible, so that our representation of agents' dispositions to believe coincides with the notion of a conditional probability system (or CPS), due to Alfred Renyi [26],1 and the elements of the "universal" 'Myerson [20] pioneered the use of CPSs in game theory.
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