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Subgame-Perfect Equilibria in Stochastic Timing Games

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  • Riedel, Frank

    (Center for Mathematical Economics, Bielefeld University)

  • Steg, Jan-Henrik

    (Center for Mathematical Economics, Bielefeld University)

Abstract

We introduce a notion of subgames for stochastic timing games and the related notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of subgame-perfect equilibrium for continuous-time games is not available in general, we argue that our model is the appropriate version for timing games. We show that the notion coincides with the usual one for discrete-time games. Many timing games in continuous time have only equilibria in mixed strategies – in particular preemption games, which often occur in the strategic real option literature. We provide a sound foundation for some workhorse equilibria of that literature, which has been lacking as we show. We obtain a general constructive existence result for subgame-perfect equilibria in preemption games and illustrate our findings by several explicit applications.

Suggested Citation

  • Riedel, Frank & Steg, Jan-Henrik, 2014. "Subgame-Perfect Equilibria in Stochastic Timing Games," Center for Mathematical Economics Working Papers 524, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:524
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    File URL: https://pub.uni-bielefeld.de/download/2698773/2902679
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    References listed on IDEAS

    as
    1. Thijssen, Jacco J.J. & Huisman, Kuno J.M. & Kort, Peter M., 2012. "Symmetric equilibrium strategies in game theoretic real option models," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 219-225.
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    3. Hendricks, Ken & Weiss, Andrew & Wilson, Charles A, 1988. "The War of Attrition in Continuous Time with Complete Information," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 663-680, November.
    4. Jan-Henrik Steg, 2015. "Preemptive Investment under Uncertainty," Papers 1511.03863, arXiv.org, revised May 2016.
    5. Simon, Leo K., 1987. "Basic Timing Games," Department of Economics, Working Paper Series qt8kt5h29p, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    6. Laraki, Rida & Solan, Eilon & Vieille, Nicolas, 2005. "Continuous-time games of timing," Journal of Economic Theory, Elsevier, vol. 120(2), pages 206-238, February.
    7. Drew Fudenberg & Jean Tirole, 1985. "Preemption and Rent Equalization in the Adoption of New Technology," Review of Economic Studies, Oxford University Press, vol. 52(3), pages 383-401.
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    11. Said Hamadène & Mohammed Hassani, 2014. "The multi-player nonzero-sum Dynkin game in discrete time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 179-194, April.
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    13. Steg, Jan-Henrik, 2016. "On preemption in discrete and continuous time," Center for Mathematical Economics Working Papers 556, Center for Mathematical Economics, Bielefeld University.
    14. 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.
    15. Steg, Jan-Henrik, 2015. "Symmetric equilibria in stochastic timing games," Center for Mathematical Economics Working Papers 543, Center for Mathematical Economics, Bielefeld University.
    16. Mason, Robin & Weeds, Helen, 2010. "Investment, uncertainty and pre-emption," International Journal of Industrial Organization, Elsevier, vol. 28(3), pages 278-287, May.
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    Cited by:

    1. Jan-Henrik Steg, 2015. "Preemptive Investment under Uncertainty," Papers 1511.03863, arXiv.org, revised May 2016.
    2. Jan-Henrik Steg & Jacco Thijssen, 2015. "Quick or Persistent? Strategic Investment Demanding Versatility," Papers 1506.04698, arXiv.org.
    3. Steg, Jan-Henrik, 2015. "Symmetric equilibria in stochastic timing games," Center for Mathematical Economics Working Papers 543, Center for Mathematical Economics, Bielefeld University.
    4. de Angelis, Tiziano & Ferrari, Giorgio & Moriarty, John, 2016. "Nash equilibria of threshold type for two-player nonzero-sum games of stopping," Center for Mathematical Economics Working Papers 563, Center for Mathematical Economics, Bielefeld University.
    5. Hellmann, Tobias & Thijssen, Jacco J.J., 2016. "Fear of the market or fear of the competitor? Ambiguity in a real options game," Center for Mathematical Economics Working Papers 533, Center for Mathematical Economics, Bielefeld University.

    More about this item

    Keywords

    timing games; stochastic games; mixed strategies; subgame-perfect equilibrium in continuous time; optimal stopping;

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