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Approximate Purification of Mixed Strategies


  • R. J. Aumann

    (The Hebrew University of Jerusalem)

  • Y. Katznelson

    (The Hebrew University of Jerusalem)

  • R. Radner

    (Bell Laboratories, 600 Mountain Avenue, Room 2C-121, Murray Hill, New Jersey 07974)

  • R. W. Rosenthal

    (Bell Laboratories, 600 Mountain Avenue, Room 2C-121, Murray Hill, New Jersey 07974)

  • B. Weiss

    (The Hebrew University of Jerusalem)


Under relatively weak conditions on the information structure of a game it is shown that any mixed strategy of a player can be replaced by a certain pure strategy without affecting any player’s expected payoff appreciably, no matter what strategies the other players use. Under even weaker conditions the existence of a Nash equilibrium in mixed strategies is shown to guarantee the existence of a pure-strategy combination which is an approximate equilibrium.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormoor:v:8:y:1983:i:3:p:327-341

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    Cited by:

    1. Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 137-153, March.
    2. Wooders, Myrna & Edward Cartwright & Selten, Reinhard, 2002. "Social Conformity And Equilibrium In Pure Strategies In Games With Many Players," The Warwick Economics Research Paper Series (TWERPS) 636, University of Warwick, Department of Economics.
    3. repec:ebl:ecbull:eb-17-01000 is not listed on IDEAS
    4. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2003. "Social Conformity in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 682, University of Warwick, Department of Economics.
    5. Wooders, M. & Selten, R. & Cartwright, E., 2001. "Some First Results for Noncooperative Pregames : Social Conformity and Equilibrium in Pure Strategies," The Warwick Economics Research Paper Series (TWERPS) 589, University of Warwick, Department of Economics.

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    game theory; Nash equilibrium; pure strategies;


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