Quantitative Marketing and Economics

, Volume 10, Issue 2, pp 197–229 | Cite as

A dynamic quality ladder model with entry and exit: Exploring the equilibrium correspondence using the homotopy method

  • Ron N. BorkovskyEmail author
  • Ulrich Doraszelski
  • Yaroslav Kryukov


This paper explores the equilibrium correspondence of a dynamic quality ladder model with entry and exit using the homotopy method. This method is ideally suited for systematically investigating the economic phenomena that arise as one moves through the parameter space and is especially useful in games that have multiple equilibria. We briefly discuss the theory of the homotopy method and its application to dynamic stochastic games. We then present three main findings: First, 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, the possibility of entry and exit 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.


Quality ladder model Dynamic oligopoly Homotopy method 

JEL Classification

L13 C63 C73 



We are greatly indebted to Mark Satterthwaite, the editor, the referee, and audiences at the University of Toronto, the University of Chicago, and the Marketing Science Conference 2010 for comments and suggestions. Borkovsky and Kryukov thank the General Motors Center for Strategy in Management at Northwestern’s Kellogg School of Management for support during this project. Borkovsky gratefully acknowledges financial support from a Connaught Start-up Grant awarded by the University of Toronto. Doraszelski gratefully acknowledges financial support from the National Science Foundation under Grant No. 0615615.


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ron N. Borkovsky
    • 1
    Email author
  • Ulrich Doraszelski
    • 2
  • Yaroslav Kryukov
    • 3
  1. 1.Rotman School of ManagementUniversity of TorontoTorontoCanada
  2. 2.Wharton SchoolUniversity of PennsylvaniaPhiladelphiaUSA
  3. 3.Tepper School of BusinessCarnegie Mellon UniversityPittsburghUSA

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