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Large but finite games with asymmetric information

  • Noguchi, Mitsunori
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    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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    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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    1. 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.
    2. Mas-Colell, Andreu & Vives, Xavier, 1993. "Implementation in Economies with a Continuum of Agents," Review of Economic Studies, Wiley Blackwell, vol. 60(3), pages 613-29, July.
    3. HART, Sergiu & HILDENBRAND, Werner & KOHLBERG, Elon, . "On equilibrium allocations as distributions on the commodity space," CORE Discussion Papers RP 183, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Carmona, Guilherme, 2004. "On the Existence of Pure Strategy Nash Equilibria in Large Games," FEUNL Working Paper Series wp465, Universidade Nova de Lisboa, Faculdade de Economia.
    5. 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.
    6. Noguchi, Mitsunori, 2009. "Existence of Nash equilibria in large games," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 168-184, January.
    7. 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.
    8. Mas-Colell, Andreu, 1984. "On a theorem of Schmeidler," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 201-206, December.
    9. Ehud Kalai, 2002. "Large Robust Games," Discussion Papers 1350, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. 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.
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