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Max-convex decompositions for cooperative TU games

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  • Francesc Llerena
  • Carlos Rafels Pallarola

    (Universitat de Barcelona)

Abstract

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with nonnegative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of modular games is a set of generators of the distributive lattice of all cooperative TU games. Finally, we characterize zero-monotonic games using a strong max-convex decomposition.

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Bibliographic Info

Paper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 123.

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Length: 14 pages
Date of creation: 2004
Date of revision:
Handle: RePEc:bar:bedcje:2004123

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Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques. Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona. Spain.
Web page: http://www.ere.ub.es
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  1. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer, vol. 29(1), pages 23-38.
  2. Curiel, I. & Tijs, S.H., 1991. "Minimarg and the maximarg operators," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154226, Tilburg University.
  3. Lucas, William F., 1992. "Von Neumann-Morgenstern stable sets," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 17, pages 543-590 Elsevier.
  4. Einy, Ezra, 1988. "The shapley value on some lattices of monotonic games," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 1-10, February.
  5. Ehud Kalai & Eitan Zemel, 1980. "On Totally Balanced Games and Games of Flow," Discussion Papers 413, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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