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Existence of Nash equilibria in large games

  • Noguchi, Mitsunori
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    Podczeck [Podczeck, K., 1997. Markets with infinitely many commodities and a continuum of agents with non-convex preferences. Economic Theory 9, 385-426] provided a mathematical formulation of the notion of "many economic agents of almost every type" and utilized this formulation as a sufficient condition for the existence of Walras equilibria in an exchange economy with a continuum of agents and an infinite dimensional commodity space. The primary objective of this article is to demonstrate that a variant of Podczeck's condition provides a sufficient condition for the existence of pure-strategy Nash equilibria in a large non-anonymous game G when defined on an atomless probability space not necessary rich, and equipped with a common uncountable compact metric space of actions A. We also investigate to see whether the condition can be applied as well to the broader context of Bayesian equilibria and prove an analogue of Yannelis's results [Yannelis, N.C., in press. Debreu's social equilibrium theorem with asymmetric information and a continuum of agents. Economic Theory] on Debreu's social equilibrium theorem with asymmetric information and a continuum of agents.

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    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 45 (2009)
    Issue (Month): 1-2 (January)
    Pages: 168-184

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    Handle: RePEc:eee:mateco:v:45:y:2009:i:1-2:p:168-184
    Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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    1. Khan, A. & Sun, Y., 2000. "Non-Cooperative Games with Many Players," Papiers d'Economie Mathématique et Applications 2000.80, Université Panthéon-Sorbonne (Paris 1).
    2. Konard Podczeck, 1997. "Markets with infinitely many commodities and a continuum of agents with non-convex preferences (*)," Economic Theory, Springer, vol. 9(3), pages 385-426.
    3. Hart, Sergiu & Hildenbrand, Werner & Kohlberg, Elon, 1974. "On equilibrium allocations as distributions on the commodity space," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 159-166, August.
    4. Podczeck, Konrad, 2008. "On the convexity and compactness of the integral of a Banach space valued correspondence," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 836-852, July.
    5. M Ali Khan & Kali P Rath & Yeneng Sun, 1998. "Pure-Strategy Nash Equilibrium Points in Large Non-Anonymous Games," Economics Working Paper Archive 393, The Johns Hopkins University,Department of Economics.
    6. Balder, Erik J., 2008. "More on equilibria in competitive markets with externalities and a continuum of agents," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 575-602, July.
    7. Balder, Erik J & Yannelis, Nicholas C, 1993. "On the Continuity of Expected Utility," Economic Theory, Springer, vol. 3(4), pages 625-43, October.
    8. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    9. Bernard Cornet & Mihaela Topuzu, 2005. "Existence of equilibria for economies with externalities and a measure space of consumers," Economic Theory, Springer, vol. 26(2), pages 397-421, 08.
    10. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May.
    11. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
    12. Zame, William R. & Noguchi, Mitsunori, 2006. "Competitive markets with externalities," Theoretical Economics, Econometric Society, vol. 1(2), pages 143-166, June.
    13. Sun, Yeneng & Yannelis, Nicholas C., 2008. "Saturation and the integration of Banach valued correspondences," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 861-865, July.
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