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Racing under uncertainty: Boundary value problem approach

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  • Cao, Dan

Abstract

This paper explores the continuous time and continuous space model of racing under uncertainty put forward by Budd, Harris, and Vickers [4] and allows for potentially asymmetric players. To prove the existence of Markov perfect equilibria, I use a boundary value problem formulation which is novel to the dynamic competition literature. In addition, by providing a new and intuitive definition of the pivot of an equilibrium, I show that equilibrium strategies exhibit the discouragement effect similar to that of Harris and Vickers [10] but under a more general class of the cost functions.

Suggested Citation

  • Cao, Dan, 2014. "Racing under uncertainty: Boundary value problem approach," Journal of Economic Theory, Elsevier, vol. 151(C), pages 508-527.
    • Handle: RePEc:eee:jetheo:v:151:y:2014:i:c:p:508-527
    DOI: 10.1016/j.jet.2013.12.002
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    References listed on IDEAS

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    1. Daron Acemoglu & Ufuk Akcigit, 2012. "Intellectual Property Rights Policy, Competition And Innovation," Journal of the European Economic Association, European Economic Association, vol. 10(1), pages 1-42, February.
    2. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    3. Philippe Aghion & Christopher Harris & Peter Howitt & John Vickers, 2001. "Competition, Imitation and Growth with Step-by-Step Innovation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 467-492.
    4. George Georgiadis, 2015. "Projects and Team Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(1), pages 187-218.
    5. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 1-21.
    6. Christopher Harris & John Vickers, 1985. "Perfect Equilibrium in a Model of a Race," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(2), pages 193-209.
    7. Christopher Budd & Christopher Harris & John Vickers, 1993. "A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 543-573.
    8. Fudenberg, Drew & Gilbert, Richard & Stiglitz, Joseph & Tirole, Jean, 1983. "Preemption, leapfrogging and competition in patent races," European Economic Review, Elsevier, vol. 22(1), pages 3-31, June.
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    Cited by:

    1. Ryota Iijima & Akitada Kasahara, 2016. "Gradual Adjustment and Equilibrium Uniqueness under Noisy Monitoring," ISER Discussion Paper 0965, Institute of Social and Economic Research, Osaka University.
    2. Dan Cao & Iván Werning, 2016. "Dynamic Savings Choices with Disagreements," NBER Working Papers 22007, National Bureau of Economic Research, Inc.
    3. Marcel Nutz & Yuchong Zhang, 2019. "A Mean Field Competition," Management Science, INFORMS, vol. 44(4), pages 1245-1263, November.
    4. Dmitry Ryvkin, 2022. "To Fight or to Give Up? Dynamic Contests with a Deadline," Management Science, INFORMS, vol. 68(11), pages 8144-8165, November.
    5. Brendan Daley & Ruoyu Wang, 2018. "When to Release Feedback in a Dynamic Tournament," Decision Analysis, INFORMS, vol. 15(1), pages 11-26, March.
    6. Marcel Nutz & Yuchong Zhang, 2017. "A Mean Field Competition," Papers 1708.01308, arXiv.org.

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    More about this item

    Keywords

    Dynamic competition; Continuous time game; Discouragement effect; Boundary value problem;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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