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Numerical solution of dynamic oligopoly games with capital investment

Author

Listed:
  • Dmitry V. Vedenov

    (Department of AED Economics, 2120 Fyffe Rd., The Ohio State University, Columbus, OH 43210, USA)

  • Mario J. Miranda

    (Department of AED Economics, 2120 Fyffe Rd., The Ohio State University, Columbus, OH 43210, USA)

Abstract

This paper discusses how numerical techniques may be used to solve the simultaneous functional equations that arise in general dynamic stochastic games. Unlike the conventional linear-quadratic approach, our methods may be used to address general model specifications that may include non-quadratic objective functions, non-linear equations of motion, and constraints on decision variables. As an illustration, we apply our methods to a dynamic duopoly game in which competing firms play short-run quantity game subject to production cost that can be lowered through investment in capital stock in the long run.

Suggested Citation

  • Dmitry V. Vedenov & Mario J. Miranda, 2001. "Numerical solution of dynamic oligopoly games with capital investment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(1), pages 237-261.
    • Handle: RePEc:spr:joecth:v:18:y:2001:i:1:p:237-261
    Note: Received: June 1, 2000; revised version: December 27, 2000
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    Cited by:

    1. Bask, Mikael & Widerberg, Anna, 2009. "Market structure and the stability and volatility of electricity prices," Energy Economics, Elsevier, vol. 31(2), pages 278-288, March.
    2. Brent, Neiman, 2011. "A state-dependent model of intermediate goods pricing," Journal of International Economics, Elsevier, vol. 85(1), pages 1-13, September.
    3. Salvador Ortigueira, 2004. "Markovian Optimal Taxation," 2004 Meeting Papers 315, Society for Economic Dynamics.
    4. Salvador Ortigueira, 2006. "Markov-Perfect Optimal Taxation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(1), pages 153-178, January.
    5. Colombo, Luca & Dawid, Herbert, 2014. "Strategic location choice under dynamic oligopolistic competition and spillovers," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 288-307.
    6. Romero-Aguilar, Randall & Miranda, Mario J. & Glauber, Joseph W., 2015. "Sustainability of Regional Food Reserves When Default is Possible," 2015 Conference, August 9-14, 2015, Milan, Italy 211825, International Association of Agricultural Economists.
    7. Brent, Neiman, 2011. "A state-dependent model of intermediate goods pricing," Journal of International Economics, Elsevier, vol. 85(1), pages 1-13, September.
    8. Chavas, Jean-Paul, 2006. "On Storage Behavior Under Imperfect Competition," Working Papers 201527, University of Wisconsin-Madison, Department of Agricultural and Applied Economics, Food System Research Group.
    9. Herbert Dawid & Michel Y. Keoula & Peter M. Kort, 2017. "Numerical Analysis of Markov-Perfect Equilibria with Multiple Stable Steady States: A Duopoly Application with Innovative Firms," Dynamic Games and Applications, Springer, vol. 7(4), pages 555-577, December.
    10. Thille, Henry, 2006. "Inventories, market structure, and price volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 30(7), pages 1081-1104, July.
    11. Koulovatianos, Christos & Mirman, Leonard J., 2007. "The effects of market structure on industry growth: Rivalrous non-excludable capital," Journal of Economic Theory, Elsevier, vol. 133(1), pages 199-218, March.
    12. Fabio Lamantia, 2011. "A Nonlinear Duopoly with Efficient Production-Capacity Levels," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 295-309, October.
    13. Yepes Rodríguez, R., 2005. "Análisis mediante teoría de juegos de la evolución de la competencia en el sector eléctrico español/Game theoretic analysis of the evolution of competition in Spanish power sector," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 23, pages 335-362, Agosto.
    14. Dawid, Herbert & Keoula, Michel Y. & Kopel, Michael & Kort, Peter M., 2023. "Dynamic investment strategies and leadership in product innovation," European Journal of Operational Research, Elsevier, vol. 306(1), pages 431-447.
    15. Hebert Dawid & Benteng Zou, 2014. "Foreign direct investment in duopoly: When is it optimal to invest abroad?," DEM Discussion Paper Series 14-23, Department of Economics at the University of Luxembourg.
    16. Herbert Dawid & Benteng Zou, 2017. "Foreign Direct Investment with Endogenous Technology Choice," Pacific Economic Review, Wiley Blackwell, vol. 22(1), pages 3-22, February.
    17. Msangi, Siwa, 2005. "Measuring the Gains to Groundwater Management with Recursive Utility," 2005 Annual meeting, July 24-27, Providence, RI 19212, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    18. Jean-Paul Chavas, 2008. "On Storage Behavior Under Imperfect Competition, with Application to the American Cheese Market," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 33(4), pages 325-339, December.
    19. Herbert Dawid & Maurizio Falcone, 2017. "Preface: DGAA Special Issue on Numerical Methods for Dynamic Games," Dynamic Games and Applications, Springer, vol. 7(4), pages 531-534, December.
    20. Romero-Aguilar, Randall S. & Miranda, Mario J., 2015. "Sustainability of Regional Reserves When Default Is Possible," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205773, Agricultural and Applied Economics Association.

    More about this item

    Keywords

    Dynamic games - Oligopoly - Numerical methods - Computational economics.;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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

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