IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/6212.html
   My bibliography  Save this paper

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

Author

Listed:
  • Doraszelski, Ulrich
  • Satterthwaite, Mark

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 & Satterthwaite, Mark, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," CEPR Discussion Papers 6212, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:6212
    as

    Download full text from publisher

    File URL: http://www.cepr.org/active/publications/discussion_papers/dp.php?dpno=6212
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    2. Robert Wilson, 2010. "Computing Equilibria of n-person Games," Levine's Working Paper Archive 402, David K. Levine.
    3. Rust, J., 1991. "Estimation of dynamic Structural Models: Problems and Prospects Part I : Discrete Decision Processes," Working papers 9106, Wisconsin Madison - Social Systems.
    4. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832 Elsevier.
    5. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Oxford University Press, vol. 62(1), pages 53-82.
    6. Herings, P. Jean-Jacques & Peeters, Ronald J. A. P., 2004. "Stationary equilibria in stochastic games: structure, selection, and computation," Journal of Economic Theory, Elsevier, vol. 118(1), pages 32-60, September.
    7. Jiawei Chen & Ulrich Doraszelski & Joseph E. Harrington, Jr., 2009. "Avoiding market dominance: product compatibility in markets with network effects," RAND Journal of Economics, RAND Corporation, vol. 40(3), pages 455-485.
    8. C. Lanier Benkard, 2004. "A Dynamic Analysis of the Market for Wide-Bodied Commercial Aircraft," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 581-611.
    9. Cabral, Luis M B & Riordan, Michael H, 1994. "The Learning Curve, Market Dominance, and Predatory Pricing," Econometrica, Econometric Society, vol. 62(5), pages 1115-1140, September.
    10. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    11. Hans Haller & Roger Lagunoff, 2000. "Genericity and Markovian Behavior in Stochastic Games," Econometrica, Econometric Society, vol. 68(5), pages 1231-1248, September.
    12. Paul Ellickson & Beresteanu Arie, 2005. "The Dynamics of Retail Oligopolies," 2005 Meeting Papers 829, Society for Economic Dynamics.
    13. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    14. Curtat, Laurent O., 1996. "Markov Equilibria of Stochastic Games with Complementarities," Games and Economic Behavior, Elsevier, vol. 17(2), pages 177-199, December.
    15. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics,in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier.
    16. Govindan, Srihari & Wilson, Robert, 2004. "Computing Nash equilibria by iterated polymatrix approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1229-1241, April.
    17. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
    18. Pakes, Ariel & McGuire, Paul, 2001. "Stochastic Algorithms, Symmetric Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Econometrica, Econometric Society, vol. 69(5), pages 1261-1281, September.
    19. Allan Collard-Wexler, 2006. "Plant Turnover and Demand Fluctuations in the Ready-Mix Concrete Industry," Working Papers 06-08, Center for Economic Studies, U.S. Census Bureau.
    20. Govindan, Srihari & Wilson, Robert, 2003. "A global Newton method to compute Nash equilibria," Journal of Economic Theory, Elsevier, vol. 110(1), pages 65-86, May.
    21. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 1-21.
    22. Chakrabarti, Subir K., 2003. "Pure strategy Markov equilibrium in stochastic games with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 693-724, September.
    23. Ronald L. Goettler & Christine A. Parlour & Uday Rajan, 2005. "Equilibrium in a Dynamic Limit Order Market," Journal of Finance, American Finance Association, vol. 60(5), pages 2149-2192, October.
    24. Gowrisankaran, Gautam, 1999. "Efficient representation of state spaces for some dynamic models," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1077-1098, August.
    25. Fudenberg, Drew & Gilbert, Richard & Stiglitz, Joseph & Tirole, Jean, 1983. "Preemption, leapfrogging and competition in patent races," European Economic Review, Elsevier, vol. 22(1), pages 3-31, June.
    26. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    27. Gautam Gowrisankaran & Robert J. Town, 1997. "Dynamic Equilibrium in the Hospital Industry," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(1), pages 45-74, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    2. Aguirregabiria, Victor & Ho, Chun-Yu, 2012. "A dynamic oligopoly game of the US airline industry: Estimation and policy experiments," Journal of Econometrics, Elsevier, vol. 168(1), pages 156-173.
    3. Hall, Joshua & Laincz, Christopher, 2012. "Optimal R&D Subsidies with Heterogeneous Firms in a Dynamic Setting," School of Economics Working Paper Series 2012-13, LeBow College of Business, Drexel University.
    4. Jiawei Chen & Ulrich Doraszelski & Joseph E. Harrington, Jr., 2009. "Avoiding market dominance: product compatibility in markets with network effects," RAND Journal of Economics, RAND Corporation, vol. 40(3), pages 455-485.
    5. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, June.
    6. Fershtman, Chaim & Markovich, Sarit, 2010. "Patents, imitation and licensing in an asymmetric dynamic R&D race," International Journal of Industrial Organization, Elsevier, vol. 28(2), pages 113-126, March.
    7. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    8. Wilson, Nathan E., 2012. "Uncertain regulatory timing and market dynamics," International Journal of Industrial Organization, Elsevier, vol. 30(1), pages 102-115.
    9. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
    10. Jeff Thurk, 2010. "International Protection of Intellectual Property: A Quantitative Assessment," 2010 Meeting Papers 479, Society for Economic Dynamics.
    11. Simon Mongey, 2017. "Market Structure and Monetary Non-Neutrality," 2017 Meeting Papers 184, Society for Economic Dynamics.
    12. Markovich, Sarit, 2008. "Snowball: A dynamic oligopoly model with indirect network effects," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 909-938, March.
    13. Govindan, Srihari & Wilson, Robert, 2009. "Global Newton Method for stochastic games," Journal of Economic Theory, Elsevier, vol. 144(1), pages 414-421, January.

    More about this item

    Keywords

    dynamic oligopoly; industry dynamics; Markov perfect equilibrium;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cpr:ceprdp:6212. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.