Endogenous depth of reasoning

We introduce a model of strategic thinking in games of initial response. Unlike standard level-k models, in this framework the player's `depth of reasoning' is endogenously determined, andit can be disentangled from his beliefs over his opponent's cognitive bound. In our approach,individuals act as if they follow a cost-benefit analysis. The depth of reasoning is a function ofthe player's cognitive abilities and his payoffs. The costs are exogenous and represent the gametheoretical sophistication of the player; the benefit instead is related to the game payoffs. Behavioris in turn determined by the individual's depth of reasoning and his beliefs about the reasoningprocess of the opponent. Thus, in our framework, payoffs not only affect individual choices inthe traditional sense, but they also shape the cognitive process itself. Our model delivers testableimplications on players' chosen actions as incentives and opponents change. We then test themodel's predictions with an experiment. We administer different treatments that vary beliefs overpayoffs and opponents, as well as beliefs over opponents' beliefs. The results of this experiment,which are not accounted for by current models of reasoning in games, strongly support our theory.Our approach therefore serves as a novel, unifying framework of strategic thinking that allows forpredictions across games.