IDEAS home Printed from
   My bibliography  Save this article

On Dynamic Games with Randomly Arriving Players


  • Pierre Bernhard

    () (INRIA-Sophia Antipolis Méditerranée)

  • Marc Deschamps

    () (Université de Bourgogne Franche-Comté)


Abstract We consider a dynamic game where additional players (assumed identical, even if there will be a mild departure from that hypothesis) join the game randomly according to a Bernoulli process. The problem solved here is that of computing their expected payoff as a function of time and the number of players present when they arrive, if the strategies are given. We consider both a finite horizon game and an infinite horizon, discounted game. As illustrations, we discuss some examples relating to oligopoly theory (Cournot, Stackelberg, cartel).

Suggested Citation

  • Pierre Bernhard & Marc Deschamps, 2017. "On Dynamic Games with Randomly Arriving Players," Dynamic Games and Applications, Springer, vol. 7(3), pages 360-385, September.
  • Handle: RePEc:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0197-z DOI: 10.1007/s13235-016-0197-z

    Download full text from publisher

    File URL:
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    1. De Sinopoli, Francesco & Meroni, Claudia & Pimienta, Carlos, 2014. "Strategic stability in Poisson games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 46-63.
    2. Ar. Rubinstein., 2008. "Dilemmas of an Economic Theorist," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 11.
    3. Samuelson, William F., 1985. "Competitive bidding with entry costs," Economics Letters, Elsevier, vol. 17(1-2), pages 53-57.
    4. Milchtaich, Igal, 2004. "Random-player games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 353-388, May.
    5. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    6. McAfee, R. Preston & McMillan, John, 1987. "Auctions with entry," Economics Letters, Elsevier, vol. 23(4), pages 343-347.
    7. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September.
    8. Haurie, A. & Leizarowitz, A. & van Delft, Ch., 1994. "Boundedly optimal control of piecewise deterministic systems," European Journal of Operational Research, Elsevier, vol. 73(2), pages 237-251, March.
    9. Matthews, Steven, 1987. "Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View," Econometrica, Econometric Society, vol. 55(3), pages 633-646, May.
    10. De Sinopoli, Francesco & Pimienta, Carlos, 2009. "Undominated (and) perfect equilibria in Poisson games," Games and Economic Behavior, Elsevier, vol. 66(2), pages 775-784, July.
    11. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    12. Robert Östling & Joseph Tao-yi Wang & Eileen Y. Chou & Colin F. Camerer, 2011. "Testing Game Theory in the Field: Swedish LUPI Lottery Games," American Economic Journal: Microeconomics, American Economic Association, vol. 3(3), pages 1-33, August.
    13. Levin, Dan & Ozdenoren, Emre, 2004. "Auctions with uncertain numbers of bidders," Journal of Economic Theory, Elsevier, vol. 118(2), pages 229-251, October.
    14. Makris, Miltiadis, 2008. "Complementarities and macroeconomics: Poisson games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 180-189, January.
    15. McAfee, R. Preston & McMillan, John, 1987. "Auctions with a stochastic number of bidders," Journal of Economic Theory, Elsevier, vol. 43(1), pages 1-19, October.
    16. Michèle Breton & Michel Keoula, 2012. "Farsightedness in a Coalitional Great Fish War," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 51(2), pages 297-315, February.
    17. Ritzberger, Klaus, 2009. "Price competition with population uncertainty," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 145-157, September.
    18. 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.
    19. Piccione, Michele & Tan, Guofu, 1996. "A Simple Model of Expert and Non-Expert Bidding in First-Price Auctions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 501-515, August.
    20. Andrzej Nowak & Eilon Solan & Sylvain Sorin, 2013. "Preface: Special Issue on Stochastic Games," Dynamic Games and Applications, Springer, vol. 3(2), pages 125-127, June.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

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

    More about this item


    Bernoulli process of entry; Market structure; Dynamic programming;

    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
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0197-z. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.