IDEAS home Printed from https://ideas.repec.org/p/crb/wpaper/2015-13.html
   My bibliography  Save this paper

On dynamic games with randomly arriving players

Author

Listed:
  • Pierre Bernhard

    () (BIOCORE team, INRIA Sophia Antipolis-Méditerranée)

  • Marc Deschamps

    () (CRESE, BETA-CNRS and OFCE-Sciences Po., Univ. 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, 2015. "On dynamic games with randomly arriving players," Working Papers 2015-13, CRESE.
  • Handle: RePEc:crb:wpaper:2015-13
    as

    Download full text from publisher

    File URL: https://crese.univ-fcomte.fr/uploads/wp/WP-2015-13.pdf
    File Function: First version, 2015
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Ar. Rubinstein., 2008. "Dilemmas of an Economic Theorist," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 11.
    3. Myerson, Roger B., 1998. "Extended Poisson Games and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 25(1), pages 111-131, October.
    4. De Sinopoli, Francesco & Meroni, Claudia & Pimienta, Carlos, 2014. "Strategic stability in Poisson games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 46-63.
    5. Samuelson, William F., 1985. "Competitive bidding with entry costs," Economics Letters, Elsevier, vol. 17(1-2), pages 53-57.
    6. Milchtaich, Igal, 2004. "Random-player games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 353-388, May.
    7. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(3), pages 375-392.
    8. McAfee, R. Preston & McMillan, John, 1987. "Auctions with entry," Economics Letters, Elsevier, vol. 23(4), pages 343-347.
    9. Myerson, Roger B., 2000. "Large Poisson Games," Journal of Economic Theory, Elsevier, vol. 94(1), pages 7-45, September.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. Ritzberger, Klaus, 2009. "Price competition with population uncertainty," Mathematical Social Sciences, Elsevier, vol. 58(2), pages 145-157, September.
    16. 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.
    17. 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.
    18. 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.
    19. Levin, Dan & Ozdenoren, Emre, 2004. "Auctions with uncertain numbers of bidders," Journal of Economic Theory, Elsevier, vol. 118(2), pages 229-251, October.
    20. Makris, Miltiadis, 2008. "Complementarities and macroeconomics: Poisson games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 180-189, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pierre Bernhard & Marc Deschamps, 2016. "Dynamic equilibrium in games with randomly arriving players," Working Papers 2016-10, CRESE.
    2. Boosey, Luke & Brookins, Philip & Ryvkin, Dmitry, 2017. "Contests with group size uncertainty: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 105(C), pages 212-229.
    3. Boosey, Luke & Brookins, Philip & Ryvkin, Dmitry, 2019. "Contests between groups of unknown size," Games and Economic Behavior, Elsevier, vol. 113(C), pages 756-769.
    4. Hillenbrand, Adrian & Winter, Fabian, 2018. "Volunteering under population uncertainty," Games and Economic Behavior, Elsevier, vol. 109(C), pages 65-81.
    5. Milchtaich, Igal, 2004. "Random-player games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 353-388, May.
    6. Pierre Bernhard & Marc Deschamps, 0. "Dynamic Equilibrium with Randomly Arriving Players," Dynamic Games and Applications, Springer, vol. 0, pages 1-28.
    7. De Sinopoli, Francesco & Meroni, Claudia & Pimienta, Carlos, 2014. "Strategic stability in Poisson games," Journal of Economic Theory, Elsevier, vol. 153(C), pages 46-63.
    8. repec:pit:wpaper:323 is not listed on IDEAS
    9. Flavio Menezes & Paulo Klinger Monteiro, 1996. "A Note on Auctions with Endogenous Participation," Microeconomics 9610003, University Library of Munich, Germany, revised 31 Oct 1996.
    10. Ronald M. Harstad, 2005. "Rational Participation Revolutionizes Auction Theory," Working Papers 0504, Department of Economics, University of Missouri.
    11. Meroni, Claudia & Pimienta, Carlos, 2017. "The structure of Nash equilibria in Poisson games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 128-144.
    12. Dmitry Ryvkin & Mikhail Drugov, 2017. "Tournaments," Working Papers wp2017_03_02, Department of Economics, Florida State University.
    13. 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.
    14. Drugov, Mikhail & Ryvkin, Dmitry, 2017. "Winner-Take-All Tournaments," CEPR Discussion Papers 12067, C.E.P.R. Discussion Papers.
    15. Aleksandar Saša Pekev{c} & Ilia Tsetlin, 2008. "Revenue Ranking of Discriminatory and Uniform Auctions with an Unknown Number of Bidders," Management Science, INFORMS, vol. 54(9), pages 1610-1623, September.
    16. Ronald M Harstad, 2011. "Endogenous Competition Alters the Structure of Optimal Auctions," ISER Discussion Paper 0816, Institute of Social and Economic Research, Osaka University.
    17. Levin, Dan & Ozdenoren, Emre, 2004. "Auctions with uncertain numbers of bidders," Journal of Economic Theory, Elsevier, vol. 118(2), pages 229-251, October.
    18. Diego Aycinena & Lucas Rentschler, 2018. "Auctions with endogenous participation and an uncertain number of bidders: experimental evidence," Experimental Economics, Springer;Economic Science Association, vol. 21(4), pages 924-949, December.
    19. Micael Castanheira, 2003. "Why Vote For Losers?," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1207-1238, September.
    20. Jehiel, Philippe & Lamy, Laurent, 2014. "On discrimination in procurement auctions," CEPR Discussion Papers 9790, C.E.P.R. Discussion Papers.
    21. Laurent Bouton & Micael Castanheira, 2012. "One Person, Many Votes: Divided Majority and Information Aggregation," Econometrica, Econometric Society, vol. 80(1), pages 43-87, January.

    More about this item

    Keywords

    Dynamic game; Bernoulli process of entry; Oligopoly;
    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
    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    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:crb:wpaper:2015-13. 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: (Yves Oytana). General contact details of provider: http://edirc.repec.org/data/crufcfr.html .

    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.