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Asymptotic Values of Vector Measure Games

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Author Info

  • Abraham Neyman

    ()

  • Rann Smorodinsky

    ()

Abstract

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.

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp344.

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Length: 60 pages
Date of creation: Nov 2003
Date of revision:
Publication status: Forthcoming in Mathematics of Operations Research
Handle: RePEc:huj:dispap:dp344

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Related research

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

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References

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  1. Aumann, R. J. & Kurz, M. & Neyman, A., 1987. "Power and public goods," Journal of Economic Theory, Elsevier, vol. 42(1), pages 108-127, June.
  2. Aumann, Robert J & Kurz, Mordecai, 1977. "Power and Taxes," Econometrica, Econometric Society, vol. 45(5), pages 1137-61, July.
  3. Abraham Neyman, 2001. "Singular Games in bv'NA," Discussion Paper Series dp262, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  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. Aumann, R J & Kurz, M & Neyman, A, 1983. "Voting for Public Goods," Review of Economic Studies, Wiley Blackwell, vol. 50(4), pages 677-93, October.
  6. A. W. Coats, 1996. "Introduction," History of Political Economy, Duke University Press, vol. 28(5), pages 3-11, Supplemen.
  7. 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.
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Cited by:
  1. Omer Edhan, 2012. "Values of Nondifferentiable Vector Measure Games," Discussion Paper Series dp602, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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