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Extremal Choice Equilibrium: Existence and Purification with Infinite-Dimensional Externalities

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    Abstract

    We prove existence and purification results for equilibria in which players choose extreme points of their feasible actions in a class of strategic environments exhibiting a product structure. We assume finite-dimensional action sets and allow for infinite-dimensional externalities. Applied to large games, we obtain existence of Nash equilibrium in pure strategies while allowing a continuum of groups and general dependence of payoffs on average actions across groups, without resorting to saturated measure spaces. Applied to games of incomplete information, we obtain a new purification result for Bayes-Nash equilibria that permits substantial correlation across types, without assuming conditional independence given the realization of a finite environmental state. We highlight our results in examples of industrial organization, auctions, and voting.

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    File URL: http://rcer.econ.rochester.edu/RCERPAPERS/rcer_567.pdf
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    Bibliographic Info

    Paper provided by University of Rochester - Center for Economic Research (RCER) in its series RCER Working Papers with number 567.

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    Length: 29 pages
    Date of creation: Oct 2011
    Date of revision:
    Handle: RePEc:roc:rocher:567

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    Postal: University of Rochester, Center for Economic Research, Department of Economics, Harkness 231 Rochester, New York 14627 U.S.A.

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    1. M Ali Khan & Kali P Rath & Yeneng Sun, 1994. "On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economics Working Paper Archive 381, The Johns Hopkins University,Department of Economics, revised Feb 1997.
    2. repec:bla:restud:v:73:y:2006:i:4:p:1039-1056 is not listed on IDEAS
    3. Filipe Martins-da-Rocha, V. & Topuzu, Mihaela, 2008. "Cournot-Nash equilibria in continuum games with non-ordered preferences," Journal of Economic Theory, Elsevier, vol. 140(1), pages 314-327, May.
    4. Balder, Erik J., 2002. "A Unifying Pair of Cournot-Nash Equilibrium Existence Results," Journal of Economic Theory, Elsevier, vol. 102(2), pages 437-470, February.
    5. David McAdams, 2006. "Monotone Equilibrium in Multi-Unit Auctions," Review of Economic Studies, Oxford University Press, vol. 73(4), pages 1039-1056.
    6. Rath, Kali P, 1992. "A Direct Proof of the Existence of Pure Strategy Equilibria in Games with a Continuum of Players," Economic Theory, Springer, vol. 2(3), pages 427-33, July.
    7. 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.
    8. Balder E. J. & Rustichini A., 1994. "An Equilibrium Result for Games with Private Information and Infinitely Many Players," Journal of Economic Theory, Elsevier, vol. 62(2), pages 385-393, April.
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