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Purification and Independence

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  • Michael Greinecker

    ()

  • Konrad Podczeck

    ()

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    Abstract

    We show that concepts introduced by Aumann more than thirty years ago throw a new light on purification in games with extremely dispersed private information. We show that one can embed payoff-irrelevant randomization devices in the private information of players and use these randomization devices to implement mixed strategies as deterministic functions of the private information. This approach gives rise to very short, elementary, and intuitive proofs for a number of purification results that previously required sophisticated methods from functional analysis or nonstandard analysis. We use our methods to prove a general purification theorem for games with private information in which a player's payoffs can depend in arbitrary ways on events in the private information of other players and in which we allow for shared information in a general way.

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    File URL: http://eeecon.uibk.ac.at/wopec2/repec/inn/wpaper/2013-18.pdf
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    Bibliographic Info

    Paper provided by Faculty of Economics and Statistics, University of Innsbruck in its series Working Papers with number 2013-18.

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    Length: 25
    Date of creation: Jul 2013
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    Handle: RePEc:inn:wpaper:2013-18

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    1. Carmona, Guilherme & Podczeck, Konrad, 2013. "Existence of Nash Equilibrium in games with a measure space of players and discontinuous payoff functions," MPRA Paper 44263, University Library of Munich, Germany.
    2. 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.
    3. Konrad Podczeck, 2010. "On existence of rich Fubini extensions," Economic Theory, Springer, vol. 45(1), pages 1-22, October.
    4. Wang, Jianwei & Zhang, Yongchao, 2010. "Purification, Saturation and the Exact Law of Large Numbers," MPRA Paper 22119, University Library of Munich, Germany.
    5. Rustichini, Aldo, 1993. "Mixing on Function Spaces," Economic Theory, Springer, vol. 3(1), pages 183-91, January.
    6. 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, vol. 34(1), pages 91-104, April.
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