IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v58y2010i4-part-2p1116-1132.html
   My bibliography  Save this article

A User's Guide to Solving Dynamic Stochastic Games Using the Homotopy Method

Author

Listed:
  • Ron N. Borkovsky

    (Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada)

  • Ulrich Doraszelski

    (Department of Economics, Harvard University, Cambridge, Massachusetts 02138)

  • Yaroslav Kryukov

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

Abstract

This paper provides a step-by-step guide to solving dynamic stochastic games using the homotopy method. The homotopy method facilitates exploring the equilibrium correspondence in a systematic fashion; it is especially useful in games that have multiple equilibria. We discuss the theory of the homotopy method and its implementation and present two detailed examples of dynamic stochastic games that are solved using this method.

Suggested Citation

  • Ron N. Borkovsky & Ulrich Doraszelski & Yaroslav Kryukov, 2010. "A User's Guide to Solving Dynamic Stochastic Games Using the Homotopy Method," Operations Research, INFORMS, vol. 58(4-part-2), pages 1116-1132, August.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:4-part-2:p:1116-1132
    DOI: 10.1287/opre.1100.0843
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1100.0843
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1100.0843?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. David Besanko & Ulrich Doraszelski, 2004. "Capacity Dynamics and Endogenous Asymmetries in Firm Size," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 23-49, Spring.
    2. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 119-156, January.
    3. Ariel Pakes & Paul McGuire, 1994. "Computing Markov-Perfect Nash Equilibria: Numerical Implications of a Dynamic Differentiated Product Model," RAND Journal of Economics, The RAND Corporation, vol. 25(4), pages 555-589, Winter.
    4. Doraszelski, Ulrich & Pakes, Ariel, 2007. "A Framework for Applied Dynamic Analysis in IO," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 30, pages 1887-1966, Elsevier.
    5. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    6. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov‐perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243, June.
    7. 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.
    8. David Besanko & Ulrich Doraszelski & Yaroslav Kryukov & Mark Satterthwaite, 2010. "Learning-by-Doing, Organizational Forgetting, and Industry Dynamics," Econometrica, Econometric Society, vol. 78(2), pages 453-508, March.
    9. C. B. Garcia & W. I. Zangwill, 1979. "An Approach to Homotopy and Degree Theory," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 390-405, November.
    10. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    11. Mark Armstrong & Robert Porter (ed.), 2007. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 3, number 1.
    12. Steven Berry & Ariel Pakes, 2007. "The Pure Characteristics Demand Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1193-1225, November.
    13. 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.
    14. Schmedders, Karl, 1998. "Computing equilibria in the general equilibrium model with incomplete asset markets," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1375-1401, August.
    15. H. M. Amman & D. A. Kendrick & J. Rust (ed.), 1996. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 1, number 1.
    16. Eaves, B. Curtis & Schmedders, Karl, 1999. "General equilibrium models and homotopy methods," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1249-1279, September.
    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. Steven T Berry & Giovanni Compiani, 2023. "An Instrumental Variable Approach to Dynamic Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(4), pages 1724-1758.
    2. Zaruhi Hakobyan & Christos Koulovatianos, 2021. "Symmetric Markovian Games of Commons with Potentially Sustainable Endogenous Growth," Dynamic Games and Applications, Springer, vol. 11(1), pages 54-83, March.
    3. Samano, Mario & Santugini, Marc, 2020. "Long-run market configurations in a dynamic quality-ladder model with externalities," Journal of Economic Dynamics and Control, Elsevier, vol. 117(C).
    4. David Besanko & Ulrich Doraszelski & Yaroslav Kryukov, 2017. "How Efficient is Dynamic Competition? The Case of Price as Investment," NBER Working Papers 23829, National Bureau of Economic Research, Inc.
    5. Dang, Chuangyin & Meng, Xiaoxuan & Talman, Dolf, 2015. "An Interior-Point Path-Following Method for Computing a Perfect Stationary Point of a Polynomial Mapping on a Polytope," Other publications TiSEM 07b7a0e7-f814-4ec2-a3a7-e, Tilburg University, School of Economics and Management.
    6. Pablo Schenone, 2020. "Final Topology for Preference Spaces," Papers 2004.02357, arXiv.org, revised Mar 2024.
    7. Ron N. Borkovsky & Avi Goldfarb & Avery M. Haviv & Sridhar Moorthy, 2017. "Measuring and Understanding Brand Value in a Dynamic Model of Brand Management," Marketing Science, INFORMS, vol. 36(4), pages 471-499, July.
    8. Doraszelski, Ulrich & Besanko, David & Kryukov, Yaroslav, 2017. "How Efficient is Dynamic Competition? The Case of Price as Investment," CEPR Discussion Papers 12279, C.E.P.R. Discussion Papers.
    9. Tava Lennon Olsen & Rodney P. Parker, 2014. "On Markov Equilibria in Dynamic Inventory Competition," Operations Research, INFORMS, vol. 62(2), pages 332-344, April.
    10. Cao, Yiyin & Dang, Chuangyin & Xiao, Zhongdong, 2022. "A differentiable path-following method to compute subgame perfect equilibria in stationary strategies in robust stochastic games and its applications," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1032-1050.
    11. Jean-Pierre Dubé & Xueming Luo & Zheng Fang, 2017. "Self-Signaling and Prosocial Behavior: A Cause Marketing Experiment," Marketing Science, INFORMS, vol. 36(2), pages 140-156, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Doraszelski, Ulrich & Kryukov, Yaroslav & Borkovsky, Ron N., 2008. "A User's Guide to Solving Dynamic Stochastic Games Using the Homotopy Method," CEPR Discussion Papers 6733, C.E.P.R. Discussion Papers.
    2. Ron N. Borkovsky & Ulrich Doraszelski & Yaroslav Kryukov, "undated". "A User''s Guide to Solving Dynamic Stochastic Games Using the Homotopy Method," GSIA Working Papers 2009-E23, Carnegie Mellon University, Tepper School of Business.
    3. Ron Borkovsky & Ulrich Doraszelski & Yaroslav Kryukov, 2012. "A dynamic quality ladder model with entry and exit: Exploring the equilibrium correspondence using the homotopy method," Quantitative Marketing and Economics (QME), Springer, vol. 10(2), pages 197-229, June.
    4. Gabriel Y. Weintraub & C. Lanier Benkard & Benjamin Van Roy, 2010. "Computational Methods for Oblivious Equilibrium," Operations Research, INFORMS, vol. 58(4-part-2), pages 1247-1265, August.
    5. C. Lanier Benkard & Przemyslaw Jeziorski & Gabriel Y. Weintraub, 2013. "Oblivious Equilibrium for Concentrated Industries," NBER Working Papers 19307, National Bureau of Economic Research, Inc.
    6. Ulrich Doraszelski & Kenneth L. Judd, 2012. "Avoiding the curse of dimensionality in dynamic stochastic games," Quantitative Economics, Econometric Society, vol. 3(1), pages 53-93, March.
    7. Vivek Farias & Bar Ifrach & Gabriel Weintraub, 2012. "A Framework for Dynamic Oligopoly in Concentrated Industries," 2012 Meeting Papers 505, Society for Economic Dynamics.
    8. David Besanko & Ulrich Doraszelski, 2005. "Learning-by-Doing, Organizational Forgetting, and Industry Dynanmics," Computing in Economics and Finance 2005 236, Society for Computational Economics.
    9. David Besanko & Ulrich Doraszelski & Yaroslav Kryukov & Mark Satterthwaite, 2007. "Learning-by-Doing, Organizational Forgetting, and Industry Dynamics," Levine's Bibliography 321307000000000903, UCLA Department of Economics.
    10. C. Lanier Benkard & Benjamin Van Roy & Gabriel Y. Weintraub, 2005. "Markov perfect industry dynamics with many firms," Working Paper Series 2005-23, Federal Reserve Bank of San Francisco.
    11. C. Lanier Benkard & Przemyslaw Jeziorski & Gabriel Y. Weintraub, 2015. "Oblivious equilibrium for concentrated industries," RAND Journal of Economics, RAND Corporation, vol. 46(4), pages 671-708, October.
    12. Ulrich Doraszelski & Kenneth L. Judd, 2019. "Dynamic stochastic games with random moves," Quantitative Marketing and Economics (QME), Springer, vol. 17(1), pages 59-79, March.
    13. David Besanko & Ulrich Doraszelski & Yaroslav Kryukov & Mark Satterthwaite, 2008. "Learning-by-Doing, Organizational Forgetting, and Industry Dynamics," GSIA Working Papers 2009-E22, Carnegie Mellon University, Tepper School of Business.
    14. Gabriel Weintraub & C. Lanier Benkard & Ben Van Roy, 2005. "Markov Perfect Industry Dynamics with Many Firms," NBER Working Papers 11900, National Bureau of Economic Research, Inc.
    15. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    16. Brett Hollenbeck, 2020. "Horizontal mergers and innovation in concentrated industries," Quantitative Marketing and Economics (QME), Springer, vol. 18(1), pages 1-37, March.
    17. Samano, Mario & Santugini, Marc & Zaccour, Georges, 2017. "Dynamics in research joint ventures and R&D collaborations," Journal of Economic Dynamics and Control, Elsevier, vol. 77(C), pages 70-92.
    18. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    19. Ron N. Borkovsky, 2017. "The timing of version releases: A dynamic duopoly model," Quantitative Marketing and Economics (QME), Springer, vol. 15(3), pages 187-239, September.
    20. Ronald Goettler & Brett Gordon, 2014. "Competition and product innovation in dynamic oligopoly," Quantitative Marketing and Economics (QME), Springer, vol. 12(1), pages 1-42, March.

    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:inm:oropre:v:58:y:2010:i:4-part-2:p:1116-1132. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.