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Dynamic equilibrium in games with randomly arriving players

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  • Pierre Bernhard

    (BIOCORE - Biological control of artificial ecosystems - LOV - Laboratoire d'océanographie de Villefranche - UPMC - Université Pierre et Marie Curie - Paris 6 - INSU - CNRS - Institut national des sciences de l'Univers - CNRS - Centre National de la Recherche Scientifique - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en Automatique - INRA - Institut National de la Recherche Agronomique)

  • Marc Deschamps

    (CRESE - Centre de REcherches sur les Stratégies Economiques - UFC - UBFC - Université Bourgogne Franche-Comté - UFC - Université de Franche-Comté, LCE - Laboratoire Chrono-environnement - UBFC - Université Bourgogne Franche-Comté - UFC - Université de Franche-Comté - CNRS - Centre National de la Recherche Scientifique)

Abstract

There are real strategic situations where nobody knows ex ante how many players there will be in the game at each step. Assuming that entry and exit could be modelized by random processes whose probability laws are common knowledge, we use dynamic programming and piecewise deterministic Markov decision processes to investigate such games. We study the dynamic equilibrium in games with randomly arriving players in discrete and continuous time for both finite and infinite horizon. Existence of dynamic equilibrium in discrete time is proved and we develop explicit algorithms for both discrete and continuous time linear quadratic problems. In both cases we offer a resolution for a Cournot oligopoly with sticky prices.

Suggested Citation

  • Pierre Bernhard & Marc Deschamps, 2016. "Dynamic equilibrium in games with randomly arriving players," Working Papers hal-01394813, HAL.
  • Handle: RePEc:hal:wpaper:hal-01394813
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01394813
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    References listed on IDEAS

    as
    1. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
    2. De Sinopoli, Francesco & Meroni, Claudia & Pimienta, Carlos, 2014. "Strategic stability in Poisson games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 46-63.
    3. Samuelson, William F., 1985. "Competitive bidding with entry costs," Economics Letters, Elsevier, vol. 17(1-2), pages 53-57.
    4. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    5. repec:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0197-z is not listed on IDEAS
    6. Pierre Bernhard & Marc Deschamps, 2016. "Dynamic equilibrium in games with randomly arriving players," Working Papers 2016-10, CRESE.
    7. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    8. Pierre Bernhard & Marc Deschamps, 2017. "On Dynamic Games with Randomly Arriving Players," Dynamic Games and Applications, Springer, vol. 7(3), pages 360-385, September.
    9. Michèle Breton & Lucia Sbragia & Georges Zaccour, 2010. "A Dynamic Model for International Environmental Agreements," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 45(1), pages 25-48, January.
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    Cited by:

    1. Pierre Bernhard & Marc Deschamps, 2016. "Dynamic equilibrium in games with randomly arriving players," Working Papers 2016-10, CRESE.
    2. Pierre Bernhard & Marc Deschamps, 2016. "Cournot oligopoly with randomly arriving producers," Working Papers 2016-14, CRESE.

    More about this item

    Keywords

    Nash equilibrium; Dynamic programming; Piecewise Deterministic Markov Decision Process; Cournot oligopoly; Sticky Prices.;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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