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Preemption games under Lévy uncertainty

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  • Boyarchenko, Svetlana
  • Levendorskiĭ, Sergei

Abstract

We study a stochastic version of Fudenberg–Tirole's preemption game. Two firms contemplate entering a new market with stochastic demand. Firms differ in sunk costs of entry. If the demand process has no upward jumps, the low cost firm enters first, and the high cost firm follows. If leader's optimization problem has an interior solution, the leader enters at the optimal threshold of a monopolist; otherwise, the leader enters earlier than the monopolist. If the demand admits positive jumps, then the optimal entry threshold of the leader can be lower than the monopolist's threshold even if the solution is interior; simultaneous entry can happen either as an equilibrium or a coordination failure; the high cost firm can become the leader. We characterize subgame perfect equilibrium strategies in terms of stopping times and value functions. Analytical expressions for the value functions and thresholds that define stopping times are derived.

Suggested Citation

  • Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
  • Handle: RePEc:eee:gamebe:v:88:y:2014:i:c:p:354-380
    DOI: 10.1016/j.geb.2014.10.010
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    Citations

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    Cited by:

    1. Bruno Versaevel, 2015. "Alertness, Leadership, and Nascent Market Dynamics," Dynamic Games and Applications, Springer, vol. 5(4), pages 440-466, December.
    2. Steg, Jan-Henrik, 2018. "Preemptive investment under uncertainty," Games and Economic Behavior, Elsevier, vol. 110(C), pages 90-119.
    3. Barbieri, Stefano & Konrad, Kai A. & Malueg, David A., 2019. "Preemption Contests Between Groups," CEPR Discussion Papers 13738, C.E.P.R. Discussion Papers.
    4. 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.
    5. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
    6. Jacco J.J. Thijssen, "undated". "Equilibria in Continuous Time Preemption Games with Markovian Payoffs," Discussion Papers 11/17, Department of Economics, University of York.

    More about this item

    Keywords

    Stopping time games; Preemption; Lévy uncertainty;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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