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Strategic approximations of discontinuous games

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  • Philip Reny

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Abstract

An infinite game is approximated by restricting the players to finite subsets of their pure strategy spaces. A strategic approximation of an infinite game is a countable subset of pure strategies with the property that limits of all equilibria of all sequences of approximating games whose finite strategy sets eventually include each member of the countable set must be equilibria of the infinite game. We provide conditions under which infinite games admit strategic approximations.
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Suggested Citation

  • Philip Reny, 2011. "Strategic approximations of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 17-29, September.
  • Handle: RePEc:spr:joecth:v:48:y:2011:i:1:p:17-29
    DOI: 10.1007/s00199-010-0518-1
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    File URL: http://hdl.handle.net/10.1007/s00199-010-0518-1
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    References listed on IDEAS

    as
    1. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    2. Leo K. Simon, 1987. "Games with Discontinuous Payoffs," Review of Economic Studies, Oxford University Press, vol. 54(4), pages 569-597.
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    More about this item

    Keywords

    Discontinuous games; Finite approximation; C7;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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