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Preemption Games under Levy Uncertainty

Author

Listed:
  • Svetlana Boyarchenko

    (Department of Economics, University of Texas at Austin)

  • Sergei Levendorskii

    (Department of Mathematics, University of Leicester)

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

  • Svetlana Boyarchenko & Sergei Levendorskii, 2011. "Preemption Games under Levy Uncertainty," Department of Economics Working Papers 131101, The University of Texas at Austin, Department of Economics, revised Oct 2014.
    • Handle: RePEc:tex:wpaper:131101
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    File URL: http://ssrn.com/abstract=1841823orhttp://dx.doi.org/10.2139/ssrn.1841823
    File Function: First version, 2011
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    File URL: http://ssrn.com/abstract=2513288
    File Function: Revised version, 2014
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    Cited by:

    1. Smirnov, Vladimir & Wait, Andrew, 2021. "Preemption with a second-mover advantage," Games and Economic Behavior, Elsevier, vol. 129(C), pages 294-309.
    2. Jacco J.J. Thijssen, "undated". "Equilibria in Continuous Time Preemption Games with Markovian Payoffs," Discussion Papers 11/17, Department of Economics, University of York.
    3. Bruno Versaevel, 2015. "Alertness, Leadership, and Nascent Market Dynamics," Dynamic Games and Applications, Springer, vol. 5(4), pages 440-466, December.
    4. Steg, Jan-Henrik, 2018. "Preemptive investment under uncertainty," Games and Economic Behavior, Elsevier, vol. 110(C), pages 90-119.
    5. Stefano Barbieri & Kai A. Konrad & David A. Malueg, 2020. "Preemption contests between groups," RAND Journal of Economics, RAND Corporation, vol. 51(3), pages 934-961, September.
    6. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
    7. Thomas, Caroline, 2020. "Stopping with congestion and private payoffs," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 18-42.
    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.

    More about this item

    Keywords

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    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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