Best Reply Versus Local Monopolistic Approximation in oligopoly Games

Abstract

Analyzing the stability of firms' adjustment mechanisms has been an active topic in the study of dynamic oligopoly games. This paper focuses on two boundedly rational mechanisms: the best reply mechanism and the local monopolistic approximation mechanism. A main contribution of our study is to demonstrate that the local monopolistic approximation mechanism with less information is more stable under fairly general conditions. In particular, we examine the case of quadratic cost functions with identical coefficients for the quadratic terms. In this case, we derive that the local monopolistic approximation mechanism is always locally stable in a duopoly market. Moreover, in a triopoly market, local stability of the local monopolistic approximation mechanism is guaranteed if either the price function or the cost function is strictly convex.

Keywords: Cournot Game, Oligopoly, Best Reply, Local Monopolistic Approximation, Local Stability