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Analysis of Markovian Competitive Situations using Nonatomic Games

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  • Jian Yang
Abstract
For dynamic situations where the evolution of a player's state is influenced by his own action as well as other players' states and actions, we show that equilibria derived for nonatomic games (NGs) can be used by their large finite counterparts to achieve near-equilibrium performances. We focus on the case with quite general spaces but also with independently generated shocks driving random actions and state transitions. The NG equilibria we consider are random state-to-action maps that pay no attention to players' external environments. They are adoptable by a variety of real situations where awareness of other players' states can be anywhere between full and non-existent. Transient results here also form the basis of a link between an NG's stationary equilibrium (SE) and good stationary profiles for large finite games.

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  • Jian Yang, 2015. "Analysis of Markovian Competitive Situations using Nonatomic Games," Papers 1510.06813, arXiv.org, revised Apr 2017.
    • Handle: RePEc:arx:papers:1510.06813
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    References listed on IDEAS

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    1. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
    2. Bergin, J & Bernhardt, D, 1995. "Anonymous Sequential Games: Existence and Characterization of Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 461-489, May.
    3. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    4. Mertens, J.-F. & Parthasarathy, T., 1987. "Equilibria for discounted stochastic games," LIDAM Discussion Papers CORE 1987050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Green, Edward J., 1980. "Noncooperative price taking in large dynamic markets," Journal of Economic Theory, Elsevier, vol. 22(2), pages 155-182, April.
    6. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Guilherme Carmona, 2004. "Nash equilibria of games with a continuum of players," Nova SBE Working Paper Series wp466, Universidade Nova de Lisboa, Nova School of Business and Economics.
    8. Al-Najjar, Nabil I. & Smorodinsky, Rann, 2001. "Large Nonanonymous Repeated Games," Games and Economic Behavior, Elsevier, vol. 37(1), pages 26-39, October.
    9. Green, Edward J, 1984. "Continuum and Finite-Player Noncooperative Models of Competition," Econometrica, Econometric Society, vol. 52(4), pages 975-993, July.
    10. Wen Zhao & Yu-Sheng Zheng, 2000. "Optimal Dynamic Pricing for Perishable Assets with Nonhomogeneous Demand," Management Science, INFORMS, vol. 46(3), pages 375-388, March.
    11. Eilon Solan, 1998. "Discounted Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 1010-1021, November.
    12. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    13. Feldman, Mark & Gilles, Christian, 1985. "An expository note on individual risk without aggregate uncertainty," Journal of Economic Theory, Elsevier, vol. 35(1), pages 26-32, February.
    14. Al-Najjar, Nabil I., 2008. "Large games and the law of large numbers," Games and Economic Behavior, Elsevier, vol. 64(1), pages 1-34, September.
    15. Yuri Levin & Jeff McGill & Mikhail Nediak, 2009. "Dynamic Pricing in the Presence of Strategic Consumers and Oligopolistic Competition," Management Science, INFORMS, vol. 55(1), pages 32-46, January.
    16. David Housman, 1988. "Infinite Player Noncooperative Games and the Continuity of the Nash Equilibrium Correspondence," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 488-496, August.
    17. Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2011. "Industry dynamics: Foundations for models with an infinite number of firms," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1965-1994, September.
    18. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1997. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Journal of Economic Theory, Elsevier, vol. 76(1), pages 13-46, September.
    19. Xiaowei Xu & Wallace J. Hopp, 2006. "A Monopolistic and Oligopolistic Stochastic Flow Revenue Management Model," Operations Research, INFORMS, vol. 54(6), pages 1098-1109, December.
    20. Yang, Jian, 2011. "Asymptotic interpretations for equilibria of nonatomic games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 491-499.
    21. repec:dau:papers:123456789/342 is not listed on IDEAS
    22. Sabourian, Hamid, 1990. "Anonymous repeated games with a large number of players and random outcomes," Journal of Economic Theory, Elsevier, vol. 51(1), pages 92-110, June.
    23. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
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    Cited by:

    1. Jian Yang, 2015. "A Link between Sequential Semi-anonymous Nonatomic Games and their Large Finite Counterparts," Papers 1510.06809, arXiv.org, revised Jun 2016.

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