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Convex games, clan games, and their marginal games

Author

Listed:
  • Branzei, Rodica

    (Center for Mathematical Economics, Bielefeld University)

  • Dimitrov, Dinko

    (Center for Mathematical Economics, Bielefeld University)

  • Tijs, Stef

    (Center for Mathematical Economics, Bielefeld 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 subadditive.

Suggested Citation

  • Branzei, Rodica & Dimitrov, Dinko & Tijs, Stef, 2011. "Convex games, clan games, and their marginal games," Center for Mathematical Economics Working Papers 368, Center for Mathematical Economics, Bielefeld University.
  • Handle: RePEc:bie:wpaper:368
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    File URL: https://pub.uni-bielefeld.de/download/2315498/2319804
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    References listed on IDEAS

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    1. Tijs, S.H. & Meca, A. & Lopez, M.A., 2005. "Benefit sharing in holding situations," Other publications TiSEM 718b8e18-eb6f-407b-a9cd-e, Tilburg University, School of Economics and Management.
    2. Curiel, I. & Tijs, S.H., 1991. "Minimarg and the maximarg operators," Other publications TiSEM 1f024ef6-4383-41ae-aba6-0, Tilburg University, School of Economics and Management.
    3. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
    4. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    5. 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.
    6. Brânzei, R. & Tijs, S.H. & Timmer, J.B., 2001. "Information collecting situations and bi-monotonic allocation schemes," Other publications TiSEM b1fe5187-5a46-460d-aaeb-9, Tilburg University, School of Economics and Management.
    7. Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Other publications TiSEM 1855e4e3-7392-4ef0-a073-8, Tilburg University, School of Economics and Management.
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    9. 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.
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    11. Yaron Azrieli & Ehud Lehrer, 2004. "On Concavification and Convex Games," Game Theory and Information 0408002, EconWPA.
    12. 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.
    13. 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.
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