Cognitive Imprecision and Strategic Behavior

Abstract

We propose and experimentally test a theory of strategic behavior in which players encode and process game payoffs with cognitive noise. We focus on 2 × 2 coordination games that have multiple equilibria under complete information. Introducing a small amount of cognitive noise generates a unique equilibrium where players use a simple cutoff strategy. The model further predicts stochastic and context-dependent behavior: as volatility in the environment declines, perception of payoffs becomes less noisy and, thus, actions become more sensitive to payoffs. Context-dependence arises from an efficient use of limited cognitive resources. In a pre-registered experiment, we find strong support for these predictions: the observed distribution of actions depends systematically on the payoff distribution to which a subject’s perceptual system is adapted. Moreover, response times are consistent with the cognitive mechanism we propose. Subjects exhibit longer response times when payoffs are closer to the equilibrium cutoff and when the distribution of payoffs is more volatile. Our experimental results reject a broad class of game theoretic models that do not predict context-dependent behavior and, more generally, illuminate the role that cognitive noise plays in changing the information structure in games.

Keywords: Context-Dependence, Complexity, Stochastic Choice, Coordination Games

JEL Classification: C72, C92, D91, E71