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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.

Suggested Citation

  • Khan, M. Ali & Rath, Kali P., 2009. "On games with incomplete information and the Dvoretsky-Wald-Wolfowitz theorem with countable partitions," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 830-837, December.
  • Handle: RePEc:eee:mateco:v:45:y:2009:i:12:p:830-837
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    References listed on IDEAS

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    1. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, January.
    2. Yu, Haomiao & Zhang, Zhixiang, 2007. "Pure strategy equilibria in games with countable actions," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 192-200, February.
    3. Khan, M. Ali & Rath, Kali P. & Sun, Yeneng, 1999. "On a private information game without pure strategy equilibria1," Journal of Mathematical Economics, Elsevier, vol. 31(3), pages 341-359, April.
    4. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
    5. M. Khan & Kali Rath & Yeneng Sun, 2006. "The Dvoretzky-Wald-Wolfowitz theorem and purification in atomless finite-action games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 91-104, April.
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    Citations

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    Cited by:

    1. Michael Greinecker & Konrad Podczeck, 2013. "Purification and Independence," Working Papers 2013-18, Faculty of Economics and Statistics, University of Innsbruck.
    2. 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 151501, University of Queensland, School of Economics.
    3. Jianwei Wang & Yongchao Zhang, 2012. "Purification, saturation and the exact law of large numbers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 527-545, August.
    4. Farhad Hüsseinov & Nobusumi Sagara, 2013. "Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 923-940, October.
    5. 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, vol. 50(C), pages 197-202.
    6. Khan, M. Ali & Sagara, Nobusumi, 2016. "Relaxed large economies with infinite-dimensional commodity spaces: The existence of Walrasian equilibria," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 95-107.
    7. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2016. "Savage games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    8. Michael Greinecker & Konrad Podczeck, 2015. "Purification and roulette wheels," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 255-272, February.

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