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Dynamic equilibrium in games with randomly arriving players

Author

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  • Pierre Bernhard

    (BIOCORE - Biological control of artificial ecosystems - LOV - Laboratoire d'océanographie de Villefranche - OOVM - Observatoire océanologique de Villefranche-sur-mer - UPMC - Université Pierre et Marie Curie - Paris 6 - INSU - CNRS - Institut national des sciences de l'Univers - CNRS - Centre National de la Recherche Scientifique - 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 (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

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.science/hal-01394813
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    References listed on IDEAS

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    Cited by:

    1. Pierre Bernhard & Marc Deschamps, 2021. "Dynamic Equilibrium with Randomly Arriving Players," Dynamic Games and Applications, Springer, vol. 11(2), pages 242-269, June.
    2. Pierre Bernhard & Marc Deschamps, 2016. "Cournot oligopoly with randomly arriving producers," Working Papers 2016-14, CRESE.
    3. Pierre Bernhard & Marc Deschamps, 2016. "Dynamic equilibrium in games with randomly arriving players," Working Papers 2016-10, CRESE.
    4. Pierre Bernhard & Marc Deschamps, 2020. "Le Modèle de Cournot avec entrées aléatoires de firmes," SciencePo Working papers Main hal-03547666, HAL.

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    More about this item

    Keywords

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

    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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