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Large but finite games with asymmetric information

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  • Noguchi, Mitsunori
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    Abstract

    Carmona considered an increasing sequence of finite games in each of which players are characterized by payoff functions that are restricted to vary within a uniformly equicontinuous set and choose their strategies from a common compact metric strategy set. Then Carmona proved that each finite game in an upper tail of such a sequence admits an approximate Nash equilibrium in pure strategies. Noguchi (2009) and Yannelis (2009) recently proved that a Nash equilibrium in pure strategies exists in a continuum game with asymmetric information in which players are endowed with private information, a prior probability and choose strategies that are compatible with their private information and maximize their interim expected payoffs. The aim of this paper is to extend Carmona's result to the broader context of Bayesian equilibria and demonstrate that the existence result obtained for continuum games with asymmetric information approximately holds for large but finite games belonging to an upper tail of a sequence of finite games with asymmetric information.

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    Bibliographic Info

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

    Volume (Year): 46 (2010)
    Issue (Month): 2 (March)
    Pages: 191-213

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    Handle: RePEc:eee:mateco:v:46:y:2010:i:2:p:191-213

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Nash equilibrium Approximate equilibria Large games Bayesian games Private information;

    References

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    1. Carmona, Guilherme, 2008. "Purification of Bayesian-Nash equilibria in large games with compact type and action spaces," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1302-1311, December.
    2. Vives, X. & Mas-Colell, A., 1989. "Implementation in economies with a Continuum of Agents," UFAE and IAE Working Papers 129.90, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    3. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    4. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 46, pages 1761-1808 Elsevier.
    5. Carmona, Guilherme, 2006. "On the Existence of Pure Strategy Nash Equilibria in Large Games," FEUNL Working Paper Series wp487, Universidade Nova de Lisboa, Faculdade de Economia.
    6. 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.
    7. Nicholas Yannelis, 2009. "Debreu’s social equilibrium theorem with asymmetric information and a continuum of agents," Economic Theory, Springer, vol. 38(2), pages 419-432, February.
    8. Noguchi, Mitsunori, 2009. "Existence of Nash equilibria in large games," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 168-184, January.
    9. 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.
    10. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:
    1. Martin Meier & Enrico Minelli & Herakles Polemarchakis, 2009. "Competitive Markets with Private Information on Both Sides," Working Papers 0917, University of Brescia, Department of Economics.

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