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On games with incomplete information and the Dvoretsky-Wald-Wolfowitz theorem with countable partitions

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  • Khan, M. Ali
  • Rath, Kali P.

Abstract

It has remained an open question as to whether the results of Milgrom-Weber [Milgrom, P.R., Weber, R.J., 1985. Distributional strategies for games with incomplete information. Mathematics of Operations Research 10, 619-632] are valid for action sets with a countably infinite number of elements without additional assumptions on the abstract measure space of information. In this paper, we give an affirmative answer to this question as a consequence of an extension of a theorem of Dvoretzky, Wald and Wolfowitz (henceforth DWW) due to Edwards [Edwards, D.A., 1987. On a theorem of Dvoretsky, Wald and Wolfowitz concerning Liapunov measures. Glasgow Mathematical Journal 29, 205-220]. We also present a direct elementary proof of the DWW theorem and its extension, one that may have an independent interest.

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Bibliographic Info

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

Volume (Year): 45 (2009)
Issue (Month): 12 (December)
Pages: 830-837

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Handle: RePEc:eee:mateco:v:45:y:2009:i:12:p:830-837

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

Related research

Keywords: Atomless games Independent private information Countably infinite actions Countably infinite partitions The DWW theorem;

References

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  1. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262061414, December.
  2. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 24(7), pages 633-653.
  3. Yu, Haomiao & Zhang, Zhixiang, 2007. "Pure strategy equilibria in games with countable actions," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 43(2), pages 192-200, February.
  4. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1999. "On a private information game without pure strategy equilibria1," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 31(3), pages 341-359, April.
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Cited by:
  1. Farhad Hüsseinov & Nobusumi Sagara, 2013. "Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities," Social Choice and Welfare, Springer, Springer, vol. 41(4), pages 923-940, October.
  2. Khan, M. Ali & Zhang, Yongchao, 2014. "On the existence of pure-strategy equilibria in games with private information: A complete characterization," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 50(C), pages 197-202.
  3. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2013. "Savage Games: A Theory of Strategic Interaction with Purely Subjective Uncertainty," Risk and Sustainable Management Group Working Papers, University of Queensland, School of Economics 151501, University of Queensland, School of Economics.
  4. Jianwei Wang & Yongchao Zhang, 2012. "Purification, saturation and the exact law of large numbers," Economic Theory, Springer, Springer, vol. 50(3), pages 527-545, August.
  5. Michael Greinecker & Konrad Podczeck, 2013. "Purification and Independence," Working Papers, Faculty of Economics and Statistics, University of Innsbruck 2013-18, Faculty of Economics and Statistics, University of Innsbruck.

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