Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity

47 Pages Posted: 28 Feb 2007

See all articles by Ulrich Doraszelski

Ulrich Doraszelski

Harvard University - Department of Economics; University of Pennsylvania - Business & Public Policy Department

Mark Satterthwaite

Northwestern University - Kellogg School of Management

Multiple version iconThere are 2 versions of this paper

Date Written: Febrruary 2007

Abstract

We provide a general model of dynamic competition in an oligopolistic industry with investment, entry, and exit. To ensure that there exists a computationally tractable Markov perfect equilibrium, we introduce firm heterogeneity in the form of randomly drawn, privately known scrap values and setup costs into the model. Our game of incomplete information always has an equilibrium in cutoff entry/exit strategies. In contrast, the existence of an equilibrium in the Ericson & Pakes (1995) model of industry dynamics requires admissibility of mixed entry/exit strategies, contrary to the assertion in their paper, that existing algorithms cannot cope with. In addition, we provide a condition on the model's primitives that ensures that the equilibrium is in pure investment strategies. Building on this basic existence result, we first show that a symmetric equilibrium exists under appropriate assumptions on the model's primitives. Second, we show that, as the distribution of the random scrap values/setup costs becomes degenerate, equilibria in cutoff entry/exit strategies converge to equilibria in mixed entry/exit strategies of the game of complete information. Finally, we provide the first example of multiple symmetric equilibria in this literature.

Suggested Citation

Doraszelski, Ulrich and Satterthwaite, Mark A., Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity (Febrruary 2007). Harvard Institute of Economic Research Discussion Paper No. 2130. Available at SSRN: https://ssrn.com/abstract=965734 or http://dx.doi.org/10.2139/ssrn.965734

Ulrich Doraszelski (Contact Author)

Harvard University - Department of Economics ( email )

Littauer Center
Cambridge, MA 02138
United States
617-495-2896 (Phone)
617-495-8570 (Fax)

University of Pennsylvania - Business & Public Policy Department

3641 Locust Walk
Philadelphia, PA 19104-6372
United States

Mark A. Satterthwaite

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

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