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Nash equilibrium and the law of large numbers

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  • Mario Rui Pascoa

    (Faculdade de Economia, Universidade Nova de Lisboa, Travessa EstevÇo Pinto, 1070 Lisboa, Portugal)

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    Abstract

    Pascoa (1993a) showed that the failure of the law of large numbers for a continuum of independent randomizations implies that Schmeidler's (1973) concept of a measure-valued profile function in equilibrium might not coincide with the concept of mixed strategies equilibrium of a nonatomic game. The latter should be defined as a probability measure on pure strategies profiles which is induced by the product measure of players' mixed strategies. This paper addresses existence and approximate purification of the latter and presents an assumption on continuity of payoffs that guarantees the equivalence between the two equilibrium concepts.

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    Bibliographic Info

    Article provided by Springer in its journal International Journal of Game Theory.

    Volume (Year): 27 (1998)
    Issue (Month): 1 ()
    Pages: 83-92

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    Handle: RePEc:spr:jogath:v:27:y:1998:i:1:p:83-92

    Note: Received November 1994/Revised version September 1995/Final version May 1997
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    Web page: http://link.springer.de/link/service/journals/00182/index.htm

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    Related research

    Keywords: Nash equilibrium · nonatomic game · law of large numbers;

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    Cited by:
    1. Edward Cartwright & Myrna Wooders, 2009. "On purification of equilibrium in Bayesian games and expost Nash equilibrium," International Journal of Game Theory, Springer, vol. 38(1), pages 127-136, March.
    2. Edward Cartwright & Myrna Wooders, 2009. "On equilibrium in pure strategies in games with many players," International Journal of Game Theory, Springer, vol. 38(1), pages 137-153, March.
    3. 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.
    4. M. Ali Khan & Kali P. Rath & Yeneng Sun & Haomiao Yu, 2011. "On Large Games with a Bio-Social Typology," Economics Working Paper Archive 585, The Johns Hopkins University,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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