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On the purification of mixed strategies

Author

Listed:
  • Chaowen Yu

    (Department of Economics, Keio University)

  • Yuhki Hosoya

    (Department of Economics, Kanto-Gakuin University)

  • Toru Maruyama

    (Department of Economics, Keio University)

Abstract

We try to examine examples in Aumann et al. (1983) which illuminate the impossibility of purification in a more readable setup. We also provide a rigorous proof of the possibility of approximate purifications that is suggested in Aumann et al. (1983). Further, the relationship between the concept of "conditionally atomless" and that of "weakly conditionaly atomless" is clarified.

Suggested Citation

  • Chaowen Yu & Yuhki Hosoya & Toru Maruyama, 2018. "On the purification of mixed strategies," Economics Bulletin, AccessEcon, vol. 38(3), pages 1655-1675.
    • Handle: RePEc:ebl:ecbull:eb-17-01000
    as

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    File URL: http://www.accessecon.com/Pubs/EB/2018/Volume38/EB-18-V38-I3-P155.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. R. J. Aumann & Y. Katznelson & R. Radner & R. W. Rosenthal & B. Weiss, 1983. "Approximate Purification of Mixed Strategies," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 327-341, August.
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    Cited by:

    1. Yuhki Hosoya & Chaowen Yu, 2022. "On the approximate purification of mixed strategies in games with infinite action sets," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 69-93, May.

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    More about this item

    Keywords

    exact purification; approximate purification; conditionally atomless; Prohorov metric; Wiener's theorem;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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