The Stochastic Response Dynamic: A New Approach to Learning and Computing Equilibrium in Continuous Games

This paper describes a novel approach to both learning and computing Nash equilibrium in continuous games that is especially useful for analyzing structural game theoretic models of imperfect competition and oligopoly. We depart from the methods and assumptions of the traditional “Calculus” approach to computing equilibrium. Instead, we use a new and natural interpretation of games as conditionally specified probability models to construct a simple stochastic learning process for finding a Nash equilibrium. We call this stochastic process the stochastic response dynamic because of its resemblance to the classical Cournot best response dynamic. The stochastic response dynamic has economic meaning as a formal learning model, and thus provides a rationale for equilibrium selection, which is a major problem for the empirical application of structural game theoretic models. In addition, by way of its learning path, it provides an easy guide to check for the presence of multiple equilibria in a game. Finally, unlike the Calculus approach, the stochastic response dynamic does not depend upon the differentiability properties of the utility functions and makes no resort to the first order conditions of the underlying game.