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Asymptotic Values of Vector Measure Games


  • Abraham Neyman


  • Rann Smorodinsky



The asymptotic value, introduced by Kannai in 1966, is an asymptotic approach to the notion of the Shapley value for games with infinitely many players. A vector measure game is a game v where the worth v(S) of a coalition S is a function f of ?(S) where ? is a vector measure. Special classes of vector measure games are the weighted majority games and the two-house weighted majority games where a two-house weighted majority game is a game in which a coalition is winning if and only if it is winning in two given weighted majority games. All weighted majority games have an asymptotic value. However, not all two-house weighted majority games have an asymptotic value. In this paper we prove that the existence of infinitely many atoms with sufficient variety suffice for the existence of the asymptotic value in a general class of nonsmooth vector measure games that includes in particular two-house weighted majority games.

Suggested Citation

  • Abraham Neyman & Rann Smorodinsky, 2003. "Asymptotic Values of Vector Measure Games," Discussion Paper Series dp344, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp344

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    References listed on IDEAS

    1. R. J. Aumann & M. Kurz & A. Neyman, 1983. "Voting for Public Goods," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 677-693.
    2. Abraham Neyman, 1981. "Singular Games have Asymptotic Values," Mathematics of Operations Research, INFORMS, vol. 6(2), pages 205-212, May.
    3. J. W. Milnor & L. S. Shapley, 1978. "Values of Large Games II: Oceanic Games," Mathematics of Operations Research, INFORMS, vol. 3(4), pages 290-307, November.
    4. Hart, Sergiu, 1977. "Asymptotic value of games with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 57-80, March.
    5. N. Z. Shapiro & L. S. Shapley, 1978. "Values of Large Games, I: A Limit Theorem," Mathematics of Operations Research, INFORMS, vol. 3(1), pages 1-9, February.
    6. Aumann, Robert J & Kurz, Mordecai, 1977. "Power and Taxes," Econometrica, Econometric Society, vol. 45(5), pages 1137-1161, July.
    7. Pradeep Dubey, 1980. "Asymptotic Semivalues and a Short Proof of Kannai’s Theorem," Mathematics of Operations Research, INFORMS, vol. 5(2), pages 267-270, May.
    8. Neyman, Abraham, 2002. "Values of games with infinitely many players," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 56, pages 2121-2167 Elsevier.
    9. Aumann, R. J. & Kurz, M. & Neyman, A., 1987. "Power and public goods," Journal of Economic Theory, Elsevier, vol. 42(1), pages 108-127, June.
    10. Neyman, Abraham, 2010. "Singular games in bv'NA," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 384-387, July.
    11. A. W. Coats, 1996. "Introduction," History of Political Economy, Duke University Press, vol. 28(5), pages 3-11, Supplemen.
    12. Abraham Neyman, 1988. "Weighted Majority Games Have Asymptotic Value," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 556-580, November.
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    Cited by:

    1. Omer Edhan, 2013. "Values of nondifferentiable vector measure games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 947-972, November.

    More about this item


    asymptotic value; weighted majority game; two-house weighted; majority game; vector measure game; Shapley value;

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