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Continuous-Time Option Games: Review of Models and Extensions

Author

Listed:
  • Marco Antonio Guimaraes Dias

    (PUC-Rio, Brazil)

  • Jose Paulo Teixeira

    (PUC-Rio, Brazil)

Abstract

This paper discusses a selected literature on continuous-time option games models, providing new insights and extensions. The paper analyzes both symmetrical and asymmetrical duopoly under uncertainty, including issues like preemption, non-binding collusion, perfect-Nash equilibriums, first-mover advantage, mixed strategies, probability of mistake with simultaneous exercise, competitive advantage effect, etc. In the first model, the demand follows a stochastic process, whereas in the second model the exchange rate follows a stochastic process. This paper presents two equivalent ways to calculate the leader and follower values and thresholds, the differential and the integral methods. The paper extends the Joaquin and Buttler’s model by considering mixed strategies in asymmetric duopoly and other extensions.

Suggested Citation

  • Marco Antonio Guimaraes Dias & Jose Paulo Teixeira, 2010. "Continuous-Time Option Games: Review of Models and Extensions," Multinational Finance Journal, Multinational Finance Journal, vol. 14(3-4), pages 219-254, September.
    • Handle: RePEc:mfj:journl:v:14:y:2010:i:3-4:p:219-254
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    References listed on IDEAS

    as
    1. Han T. J. Smit & L. A. Ankum, 1993. "A Real Options and Game-Theoretic Approach to," Financial Management, Financial Management Association, vol. 22(3), Fall.
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    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    6. Leland, Hayne E & Pyle, David H, 1977. "Informational Asymmetries, Financial Structure, and Financial Intermediation," Journal of Finance, American Finance Association, vol. 32(2), pages 371-387, May.
    7. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, September.
    8. Dixit, Avinash & Pindyck, Robert S & Sodal, Sigbjorn, 1999. "A Markup Interpretation of Optimal Investment Rules," Economic Journal, Royal Economic Society, vol. 109(455), pages 179-189, April.
    9. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    10. Huisman, K.J.M. & Kort, P.M., 1999. "Effects of Strategic Interactions on the Option Value of Waiting," Discussion Paper 1999-92, Tilburg University, Center for Economic Research.
    11. Octavio A. F. Tourinho., 1979. "The Option Value of Reserves of Natural Resources," Research Program in Finance Working Papers 94, University of California at Berkeley.
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    15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    17. repec:fth:tilbur:9992 is not listed on IDEAS
    18. Dutta Prajit K. & Rustichini Aldo, 1995. "(s, S) Equilibria in Stochastic Games," Journal of Economic Theory, Elsevier, vol. 67(1), pages 1-39, October.
    19. James L. Paddock & Daniel R. Siegel & James L. Smith, 1988. "Option Valuation of Claims on Real Assets: The Case of Offshore Petroleum Leases," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(3), pages 479-508.
    20. Myers, Stewart C., 1977. "Determinants of corporate borrowing," Journal of Financial Economics, Elsevier, vol. 5(2), pages 147-175, November.
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    More about this item

    Keywords

    option games; real options; game theory; duopoly under uncertainty; preemption;
    All these keywords.

    JEL classification:

    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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