A Dynamic Quality Ladder Model with Entry and Exit: Exploring the Equilibrium Correspondence Using the Homotopy Method

34 Pages Posted: 11 Jan 2010

See all articles by Ron N. Bar (formerly Borkovsky)

Ron N. Bar (formerly Borkovsky)

Independent

Ulrich Doraszelski

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

Yaroslav (Steve) Kryukov

Northwestern University - Department of Economics

Multiple version iconThere are 2 versions of this paper

Date Written: November 2009

Abstract

This paper explores the equilibrium correspondence of a dynamic quality ladder model with entry and exit using the homotopy method. The homotopy method facilitates exploring the equilibrium correspondence in a systematic fashion; it is ideally suited for investigating the economic phenomena that arise as one moves through the parameter space and is especially useful in games that have multiple equilibria. We discuss the theory of the homotopy method and its application to dynamic stochastic games. We then present the following results: First, we find that the more costly and/or less beneficial it is to achieve or maintain a given quality level, the more a leader invests in striving to induce the follower to give up; the more quickly the follower does so; and the more asymmetric is the industry structure that arises. Second, we show that the possibility of entry and exit alone gives rise to predatory and limit investment. Third, we illustrate and discuss the multiple equilibria that arise in the quality ladder model, highlighting the presence of entry and exit as a source of multiplicity.

Keywords: computation, dynamic stochastic games, homotopy method, Markov perfect equillibrium

JEL Classification: C63, C73

Suggested Citation

Bar, Ron N. and Doraszelski, Ulrich and Kryukov, Yaroslav (Steve), A Dynamic Quality Ladder Model with Entry and Exit: Exploring the Equilibrium Correspondence Using the Homotopy Method (November 2009). CEPR Discussion Paper No. DP7560, Available at SSRN: https://ssrn.com/abstract=1533165

Ulrich Doraszelski

Harvard University - Department of Economics ( email )

Littauer Center
Cambridge, MA 02138
United States
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University of Pennsylvania - Business & Public Policy Department

3641 Locust Walk
Philadelphia, PA 19104-6372
United States

Yaroslav (Steve) Kryukov

Northwestern University - Department of Economics ( email )

2003 Sheridan Road
Evanston, IL 60208
United States

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