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Leximals, the Lexicore and the Average Lexicographic Value

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  • Funaki, Y.
  • Tijs, S.H.
  • Brânzei, R.

    (Tilburg University, Center for Economic Research)

Abstract

The lexicographic vectors of a balanced game, called here leximals, are used to define a new solution concept, the lexicore, on the cone of balanced games. Properties of the lexicore and its relation with the core on some classes of games are studied. It is shown that on cones of balanced games where the core is additive, the leximals, the lexicore and the Average Lexicographic (AL-)value are additive, too. Further, it turns out that the leximals satisfy a consistency property with respect to a reduced game `a la Davis and Maschler, which implies an average consistency property of the AL-value. Explicit formulas for the AL-value on the class of k-convex games and on the class of balanced almost convex games are provided.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-97.

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Date of creation: 2007
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Handle: RePEc:dgr:kubcen:200797

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Web page: http://center.uvt.nl

Related research

Keywords: cooperative games; the core; the AL-value; the Shapley value;

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  1. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
  2. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
  3. Pradeep Dubey & Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471, Cowles Foundation for Research in Economics, Yale University.
  4. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
  5. Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154241, Tilburg University.
  6. Brânzei, R. & Tijs, S.H., 2001. "Additivity Regions for Solutions in Cooperative Game Theory," Discussion Paper 2001-81, Tilburg University, Center for Economic Research.
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Cited by:
  1. Caprari, E. & Tijs, S.H. & Torre, A., 2008. "Weighted Average Lexicographic Values for Share Sets and Balanced Cooperative Games," Discussion Paper 2008-8, Tilburg University, Center for Economic Research.

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