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Convex games, clan games, and their marginal games

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Author Info

  • Rodica Branzei

    (Faculty of Computer Science, Alexandru Ioan Cuza University)

  • Dinko Dimitrov

    ()
    (Institute of Mathematical Economics, Bielefeld University)

  • Stef Tijs

    (Department of Econometrics and Operations Research, Tilburg University)

Abstract

We provide characterizations of convex games and total clan games by using properties of their corresponding marginal games. As it turns out, a cooperative game is convex if and only if all its marginal games are superadditive, and a monotonic game satisfying the veto player property with respect to the members of a coalition C is a total clan game (with clan C) if and only if all its C-based marginal games are superadditive.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-368.pdf
File Function: First version, 2005
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 368.

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Length: 13 pages
Date of creation: Jun 2005
Date of revision:
Handle: RePEc:bie:wpaper:368

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Related research

Keywords: characterization; convex games; marginal games; subadditive games; superadditive games; total clan games;

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References

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  1. Tijs, S.H. & Meca, A. & Lopez, M.A., 2005. "Benefit sharing in holding situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-142687, Tilburg University.
  2. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
  3. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-35, May.
  4. Voorneveld, M. & Tijs, S.H. & Grahn, S., 2003. "Monotonic allocation schemes in clan games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91573, Tilburg University.
  5. 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.
  6. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
  7. 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.
  8. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
  9. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
  10. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "A New Characterization of Convex Games," Discussion Paper 2004-109, Tilburg University, Center for Economic Research.
  11. Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154246, Tilburg University.
  12. Brânzei, R. & Tijs, S.H. & Timmer, J.B., 2001. "Information collecting situations and bi-monotonic allocation schemes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-88210, Tilburg University.
  13. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "The Equal Split-Off Set for Cooperative Games," Discussion Paper 2004-110, Tilburg University, Center for Economic Research.
  14. 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.
  15. Yaron Azrieli & Ehud Lehrer, 2004. "On Concavification and Convex Games," Game Theory and Information 0408002, EconWPA.
  16. Tijs, Stef & Meca, Ana & Lopez, Marco A., 2005. "Benefit sharing in holding situations," European Journal of Operational Research, Elsevier, vol. 162(1), pages 251-269, April.
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