Endogenous Depth of Reasoning

Abstract

We introduce a model of strategic thinking in games of initial response. Unlike standard models of strategic thinking, in this framework the player’s ‘depth of reasoning’ is endogenously determined, and it can be disentangled from his beliefs over his opponent’s cognitive bound. In our approach, individuals act as if they follow a cost-benet analysis. The depth of reasoning is a function of the player’s cognitive abilities and his payos. The costs are exogenous and represent the game theoretical sophistication of the player; the benet instead is related to the game payos. Behavior is in turn determined by the individual’s depth of reasoning and his beliefs about the reasoning process of the opponent. Thus, in our framework, payos not only aect individual choices in the traditional sense, but they also shape the cognitive process itself. Our model delivers testable implications on players’ chosen actions as incentives and opponents change. We then test the model’s predictions with an experiment. We administer dierent treatments that vary beliefs over payos 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. We also show that the predictions of our model are highly consistent, both qualitatively and quantitatively, with well-known unresolved empirical puzzles. Our approach therefore serves as a novel, unifying framework of strategic thinking that allows for predictions across games.