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Subgame-perfect equilibria in stochastic timing games

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  • Riedel, Frank
  • Steg, Jan-Henrik

Abstract

We develop a notion of subgames and the related notion of subgame-perfect equilibrium – possibly in mixed strategies – for stochastic timing games. To capture all situations that can arise in continuous-time models, it is necessary to consider stopping times as the starting dates of subgames. We generalize Fudenberg and Tirole’s (Rev. Econom. Stud. 52, 383–401, 1985) mixed-strategy extensions to make them applicable to stochastic timing games and thereby provide a sound basis for subgame-perfect equilibria of preemption games. Sufficient conditions for equilibrium existence are presented, and examples illustrate their application as well as the fact that intuitive arguments can break down in the presence of stochastic processes with jumps.

Suggested Citation

  • Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
  • Handle: RePEc:eee:mateco:v:72:y:2017:i:c:p:36-50
    DOI: 10.1016/j.jmateco.2017.06.006
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Steg, Jan-Henrik & Thijssen, Jacco, 2015. "Quick or Persistent? Strategic Investment Demanding Versatility," Center for Mathematical Economics Working Papers 541, Center for Mathematical Economics, Bielefeld University.
    2. Steg, Jan-Henrik, 2018. "Preemptive investment under uncertainty," Games and Economic Behavior, Elsevier, vol. 110(C), pages 90-119.
    3. Liangchen Li & Michael Ludkovski, 2018. "Stochastic Switching Games," Papers 1807.03893, arXiv.org.
    4. Margaria, Chiara, 2020. "Learning and payoff externalities in an investment game," Games and Economic Behavior, Elsevier, vol. 119(C), pages 234-250.
    5. Jan-Henrik Steg, 2018. "On Preemption in Discrete and Continuous Time," Dynamic Games and Applications, Springer, vol. 8(4), pages 918-938, December.
    6. Huberts, N.F.D. & Dawid, H. & Huisman, K.J.M. & Kort, P.M., 2019. "Entry deterrence by timing rather than overinvestment in a strategic real options framework," European Journal of Operational Research, Elsevier, vol. 274(1), pages 165-185.
    7. Tiziano De Angelis & Nikita Merkulov & Jan Palczewski, 2020. "On the value of non-Markovian Dynkin games with partial and asymmetric information," Papers 2007.10643, arXiv.org.
    8. 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.
    9. Steg, Jan-Henrik, 2015. "Symmetric equilibria in stochastic timing games," Center for Mathematical Economics Working Papers 543, Center for Mathematical Economics, Bielefeld University.
    10. Delaney, Laura, 2019. "Symmetric equilibrium strategies in game theoretic real option models with incomplete information," Economics Letters, Elsevier, vol. 174(C), pages 42-47.
    11. 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.

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