A two tiered dynamic oligopoly model

Abstract

Dynamic oligopoly models are used in industrial organization and the management sciences to analyze diverse dynamic phenomena such as investments in R&D or capacity, the entry and exit of firms, and dynamic pricing. The applicability of these models has been severely limited, however, by the curse of dimensionality involved in the Markov perfect equilibrium (MPE) computation. In this work we introduce a new model and equilibrium concept that alleviates the curse of dimensionality. Our model focuses on "two-tiered" industries in which few "dominant" firms have a significant market share and there are many "fringe" firms with a small market share each; this is a prevalent market structure in many industries. In MPE each firm keeps track of all of its competitors' individual states, which for example, represent their quality level. In our approach each firm keeps track of the individual states of dominant firms only and of few aggregate statistics that summarize the state of fringe firms; this dramatically reduces the dimensionality of the equilibrium computation problem. We present an asymptotic result that provides a theoretical justification for our approach. We introduce an efficient algorithm to compute our equilibrium concept and report results from computational case studies that illustrate applications. Our results suggest that our approach greatly increases the applicability of dynamic oligopoly models and opens up the door to studying novel issues in industry dynamics.