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

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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.

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  • 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.
    • Handle: RePEc:cmu:gsiawp:860735799
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    File URL: http://www.andrew.cmu.edu/user/kryukov/HomotopyGuide.pdf
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    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. 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.
    3. Bajari, Patrick & Hong, Han & Krainer, John & Nekipelov, Denis, 2010. "Estimating Static Models of Strategic Interactions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 469-482.
    4. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    5. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.
    6. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    7. By Kenneth L. Judd & Karl Schmedders & Şevin Yeltekin, 2012. "Optimal Rules For Patent Races," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(1), pages 23-52, February.
    8. 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.
    9. David Besanko & Ulrich Doraszelski, 2005. "Learning-by-Doing, Organizational Forgetting, and Industry Dynanmics," Computing in Economics and Finance 2005 236, Society for Computational Economics.
    10. Karl Schmedders & Ken Judd, 2005. "A Computational Approach to Proving Uniqueness in Dynamic Games," Computing in Economics and Finance 2005 412, Society for Computational Economics.
    11. 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.
    12. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, September.
    13. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
    14. 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.
    15. Ulrich Doraszelski & Mark Satterthwaite, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," Levine's Bibliography 321307000000000912, UCLA Department of Economics.
    16. 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.
    17. Doraszelski, Ulrich & Satterthwaite, Mark, 2007. "Computable Markov-Perfect Industry Dynamics: Existence, Purification, and Multiplicity," CEPR Discussion Papers 6212, C.E.P.R. Discussion Papers.
    18. 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.
    19. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    20. 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.
    21. 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.
    22. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    23. 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.
    24. 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.
    25. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
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