Cognitive Hierarchy: A Limited Thinking Theory in Games

Strategic thinking, best-response, and mutual consistency (equilibrium) are three key modeling principles in non-cooperative game theory. Camerer, Ho and Chong (2004) relax mutual consistency to predict how players are likely to behave in one-shot games before they can learn to equilibrate. They introduce a one-parameter cognitive hierarchy (CH) model to predict behavior in one-shot games, and initial conditions in repeated games. The CH approach assumes that players use k steps of reasoning with frequency f(k). Camerer, Ho and Chong (2004) assume f(k) to be a one-parameter Poisson distribution. This paper investigates and lends support to the generality and precision of this Poisson CH model in three ways: 1. an unconstrained general distribution CH model is found to offer only marginal improvement in fit over its Poisson cousin and hence this suggests that the Poisson approximation is reasonable; 2. the steps of thinking players used in games are found to correlate with response time and schools they attend which suggests that cognitive hierarchy captures realistically a reasoning mechanism that goes on in the brain of these players; and 3. several classes of interesting economic problems, including asset pricing and business entry can be explained by the iterated reasoning of the Poisson CH model. When compared to the Quantal Response Equilibrium model which relaxes the best-response assumption of equilibrium theory, the better fit of Poisson CH model seem to suggest that mutual consistency is a more plausible assumption to relax in explaining deviation from equilibrium theory.