A Dynamic Model of Oligopolistic Market Structure, Featuring Positioning Investments

Abstract

In their efforts to create and maintain a position in a market, firms make positioning investments of various sorts, in R&D, plant, advertising, and location, or more generally, in product development and maintenance. In an environment where the success of positioning investments is stochastic, the positioning game played by firms that compete to serve a market is necessarily dynamic. We model the positioning and operating decisions of firms in an environment of this sort. When the market is large enough to support at least one active firm, in the steady state equilibrium, the expected number of firms serving the market at a point in time is a nearly continuous function of market size, in sharp contrast to the familiar integer-valued step function seen in classic models, and expected total and consumer surplus are higher than standard non-stochastic models would indicate. This suggests that the classic models are not always a sound guide for policy.

Key Words:

• Firm Dynamics
• Positioning Investments
• Market Structure
• Oligopoly Theory
• Dynamic Oligopoly
• Markov Perfect Equilibrium.

JEL classifications:

• D4
• L13
• L11.

The authors gratefully acknowledge the helpful suggestions received in the refereeing process and the generous financial support of the Curtin University Business School (under the School’s Visiting Fellows Program) and the University of Calgary. Excellent research assistance from Maria Mangano and Alan Liang is also gratefully acknowledged. Maria Mangano's assistance was funded by a grant from the Australian Research Council.

Notes

1. This positioning technology does not allow a firm to influence the probabilities of success, P and Q, by varying the magnitudes of I and J. That is, P, Q, I, and J are exogenous parameters. We adopt this somewhat restrictive positioning technology to keep the model tractable.

2. Parameter values used in the simulations are presented in Tables 2 and 3 and are from the Baseline Model, discussed in Section 3.

3. The operating profit of an established firm is positive because the marginal cost of producing goods is assumed to be 0, and demand parameter α and market size Z are assumed to be positive.

4. See Appendix I for details of the full commitment calculations, and for a discussion of the steady state.