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

Author

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  • 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
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    References listed on IDEAS

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    Cited by:

    1. 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," Discussion Paper 2015-019, Tilburg University, Center for Economic Research.
    2. 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.
    3. 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.
    4. Pablo Schenone, 2020. "Final Topology for Preference Spaces," Papers 2004.02357, arXiv.org, revised Mar 2024.
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    6. 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).
    7. Tava Lennon Olsen & Rodney P. Parker, 2014. "On Markov Equilibria in Dynamic Inventory Competition," Operations Research, INFORMS, vol. 62(2), pages 332-344, April.
    8. 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.
    9. 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.
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    11. 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.

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