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Asymptotic Values of Vector Measure Games

Author

Listed:
  • Abraham Neyman

    () (Institute of Mathematics and Center for the Study of Rationality, Hebrew University, 91904 Jerusalem, Israel)

  • Rann Smorodinsky

    () (Davidson Faculty of Industrial Engineering and Management, Technion, 32000 Haifa, Israel)

Abstract

In honor of L. S. Shapley's eightieth birthday 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 μ( S ) where μ 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, 2004. "Asymptotic Values of Vector Measure Games," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 739-775, November.
  • Handle: RePEc:inm:ormoor:v:29:y:2004:i:4:p:739-775
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    File URL: http://dx.doi.org/10.1287/moor.1040.0118
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    References listed on IDEAS

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    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. Hart, Sergiu, 1977. "Asymptotic value of games with a continuum of players," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 57-80, March.
    3. Aumann, Robert J & Kurz, Mordecai, 1977. "Power and Taxes," Econometrica, Econometric Society, vol. 45(5), pages 1137-1161, July.
    4. 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.
    5. Aumann, R. J. & Kurz, M. & Neyman, A., 1987. "Power and public goods," Journal of Economic Theory, Elsevier, vol. 42(1), pages 108-127, June.
    6. Neyman, Abraham, 2010. "Singular games in bv'NA," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 384-387, July.
    7. A. W. Coats, 1996. "Introduction," History of Political Economy, Duke University Press, vol. 28(5), pages 3-11, Supplemen.
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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.

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