Strategies and interactive beliefs in dynamic games

Interactive epistemology in dynamic games studies forms of strategic reasoning like backward induction and forward induction by formally representing the 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. In this literature, strategies are interpreted as objective descriptions of what the players would choose at each history. 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 behavior is described only by the play path, and players' beliefs include their contingent plans. We define rational planning, a property of beliefs only, and material consistency, which connects plans with choices on the 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 induction and forward induction. We relate our work to the existing literature, and we discuss the extension of our analysis to games with imperfect information.