Strategies and interactive beliefs in dynamic games
نویسندگان
چکیده
Interactive epistemology in dynamic games studies forms of strategic reasoning like backward and forward induction by means of a formal representation of players’ beliefs about each other, conditional on each history. Work on this topic typically relies on epistemic models where states of the world specify both strategies and beliefs. Strategies are conjunctions of behavioral conditionals of the form “if history h occurred, then player i would choose action ai.” In this literature, strategies are literally interpreted as (objective) behavioral conditionals. But the intuitive interpretation of “strategy” is that of (subjective) “contingent plan of action.” As players do not delegate their moves to devices that mechanically execute a strategy, plans cannot be anything but beliefs of players about their own behavior. In this paper we analyze strategic reasoning in dynamic games with perfect information by means of epistemic models where states of the world describe the actual play path (not behavioral conditionals) and the players’ conditional probability systems about the path and about each other conditional beliefs. Therefore, the players’ beliefs include their contingent plans. We define rational planning as a property of beliefs, whereas material consistency connects plans with choices on the actual play path. Material rationality is the conjunction of rational planning and material consistency. In perfect information games of depth two (the simplest dynamic games), correct belief in material rationality only implies a Nash outcome, not the backward induction one. We have to consider stronger assumptions of persistence of belief in material rationality in order to obtain backward and forward induction reasoning.
منابع مشابه
Additional Material on “Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games”
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