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On preemption in discrete and continuous time

Author

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  • Steg, Jan-Henrik

    (Center for Mathematical Economics, Bielefeld University)

Abstract

The seminal work of Fudenberg and Tirole (1985) on how preemption erodes the value of an option to wait raises general questions about the relation between models in discrete and continuous time and thus about the interpretation of its central result, relying on an “infinitely fine grid”. Here it is shown that the preemption equilibrium is the limit of the unique symmetric equilibria of the game when reduced to any sequence of grids becoming infinitely fine. Furthermore, additional subgame perfect equilibria using conventional continuous-time mixed strategies are identified.

Suggested Citation

  • Steg, Jan-Henrik, 2016. "On preemption in discrete and continuous time," Center for Mathematical Economics Working Papers 556, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:556
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    References listed on IDEAS

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    1. Jennifer F. Reinganum, 1981. "On the Diffusion of New Technology: A Game Theoretic Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(3), pages 395-405.
    2. Drew Fudenberg & David Levine, 2008. "Limit Games and Limit Equilibria," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 2, pages 21-39, World Scientific Publishing Co. Pte. Ltd..
    3. Laraki, Rida & Solan, Eilon & Vieille, Nicolas, 2005. "Continuous-time games of timing," Journal of Economic Theory, Elsevier, vol. 120(2), pages 206-238, February.
    4. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
    5. Simon, Leo K & Stinchcombe, Maxwell B, 1989. "Extensive Form Games in Continuous Time: Pure Strategies," Econometrica, Econometric Society, vol. 57(5), pages 1171-1214, September.
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    7. Abraham Neyman, 2013. "Stochastic Games with Short-Stage Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 236-278, June.
    8. Drew Fudenberg & Jean Tirole, 1985. "Preemption and Rent Equalization in the Adoption of New Technology," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(3), pages 383-401.
    9. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.
    10. Helen Weeds, 2002. "Strategic Delay in a Real Options Model of R&D Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 729-747.
    11. Azevedo, Alcino & Paxson, Dean, 2014. "Developing real option game models," European Journal of Operational Research, Elsevier, vol. 237(3), pages 909-920.
    12. Sylvain Sorin & Guillaume Vigeral, 2016. "Operator approach to values of stochastic games with varying stage duration," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 389-410, March.
    13. Grenadier, Steven R, 1996. "The Strategic Exercise of Options: Development Cascades and Overbuilding in Real Estate Markets," Journal of Finance, American Finance Association, vol. 51(5), pages 1653-1679, December.
    14. Drew Fudenberg & David K. Levine, 2009. "Repeated Games with Frequent Signals," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 124(1), pages 233-265.
    15. Hoppe, Heidrun C. & Lehmann-Grube, Ulrich, 2005. "Innovation timing games: a general framework with applications," Journal of Economic Theory, Elsevier, vol. 121(1), pages 30-50, March.
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    Cited by:

    1. Whitmeyer Mark, 2018. "A Competitive Optimal Stopping Game," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(1), pages 1-15, January.
    2. E. Emanuel Rapsch, 2024. "Decision making in stochastic extensive form I: Stochastic decision forests," Papers 2404.12332, arXiv.org.
    3. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.

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    Keywords

    Preemption; discrete time; continuous time; subgame perfect equilibrium; convergence;
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