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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. Yaron Azrieli & Ehud Lehrer, 2004. "On Concavification and Convex Games," Game Theory and Information, EconWPA 0408002, EconWPA.
  2. Pradeep Dubey & Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 471, Cowles Foundation for Research in Economics, Yale University.
  3. Tijs, Stef & Meca, Ana & Lopez, Marco A., 2005. "Benefit sharing in holding situations," European Journal of Operational Research, Elsevier, Elsevier, vol. 162(1), pages 251-269, April.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, Elsevier, vol. 28(1), pages 1-12, July.
  9. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 615-35, May.
  10. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "A New Characterization of Convex Games," Discussion Paper, Tilburg University, Center for Economic Research 2004-109, Tilburg University, Center for Economic Research.
  11. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, Elsevier, vol. 1(3), pages 275-293, September.
  12. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, Elsevier, vol. 25(2), pages 283-286, October.
  13. 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.
  14. 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.
  15. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, Elsevier, vol. 2(4), pages 378-394, December.
  16. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2004. "The Equal Split-Off Set for Cooperative Games," Discussion Paper, Tilburg University, Center for Economic Research 2004-110, Tilburg University, Center for Economic Research.
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