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Dynamic Equilibrium with Randomly Arriving Players

Author

Listed:
  • Pierre Bernhard

    (UCA-INRIA Sophia Antipolis)

  • Marc Deschamps

    (Université de Bourgogne Franche Comté)

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 modeled 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 these games in discrete and continuous time for both finite and infinite horizon. While existence of dynamic equilibrium in discrete time is proved, our main aim is to develop algorithms. In the general nonlinear case, the equations provided are rather intricate. We develop more explicit algorithms for both discrete and continuous time linear quadratic problems.

Suggested Citation

  • Pierre Bernhard & Marc Deschamps, 2021. "Dynamic Equilibrium with Randomly Arriving Players," Dynamic Games and Applications, Springer, vol. 11(2), pages 242-269, June.
    • Handle: RePEc:spr:dyngam:v:11:y:2021:i:2:d:10.1007_s13235-020-00354-z
    DOI: 10.1007/s13235-020-00354-z
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    References listed on IDEAS

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    1. Gensbittel, Fabien & Lovo, Stefano & Renault, Jérôme & Tomala, Tristan, 2018. "Zero-sum revision games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 504-522.
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    8. Romain Biard & Marc Deschamps, 2020. "Quel impact pour les taxis si la loi supprimait toute différence règlementaire entre taxis et VTC ?," Working Papers 2020-03, CRESE.
    9. Samuelson, William F., 1985. "Competitive bidding with entry costs," Economics Letters, Elsevier, vol. 17(1-2), pages 53-57.
    10. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    11. Pierre Bernhard & Marc Deschamps, 2016. "Cournot oligopoly with randomly arriving producers," Working Papers 2016-14, CRESE.
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    Cited by:

    1. Romain Biard & Marc Deschamps & Mostapha Diss & Alexis Roussel, 2024. "Assessing Available Care Time and Nursing Shortage in a Hospital," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 26(02), pages 1-26, June.
    2. Francesco Sinopoli & Christopher Künstler & Claudia Meroni & Carlos Pimienta, 2023. "Poisson–Cournot games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(3), pages 803-840, April.
      • Francesco De Sinopoli & Christopher Kunstler & Claudia Meroni & Carlos Pimienta, 2020. "Poisson-Cournot Games," Discussion Papers 2020-07, School of Economics, The University of New South Wales.

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