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Purification and roulette wheels

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  • Michael Greinecker
  • Konrad Podczeck

Abstract

We use concepts introduced by Aumann more than 30 years ago to throw 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 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 the first 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. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:58:y:2015:i:2:p:255-272
    DOI: 10.1007/s00199-014-0815-1
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    References listed on IDEAS

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    Cited by:

    1. Khan, M. Ali & Zhang, Yongchao, 2018. "On pure-strategy equilibria in games with correlated information," Games and Economic Behavior, Elsevier, vol. 111(C), pages 289-304.

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    More about this item

    Keywords

    Purification; Games with incomplete information; Roulette wheels; C72;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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