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C-complete sets for compromise stable games


  • Platz, Trine Tornøe

    () (Department of Business and Economics)

  • Hamers, Herbert

    () (Department of Econometrics & OR and CentER)

  • Quant, Marieke

    (Department of Econometrics & OR and CentER)


The core cover of a TU-game is a superset of the core and equals the convex hull of its larginal vectors. A larginal vector corresponds to an ordering of the players and describes the efficient payoff vector giving the first players in the ordering their utopia demand as long as it is still possible to assign the remaining players at least their minimum right. A game is called compromise stable if the core is equal to the core cover, i.e. the core is the convex hull of the larginal vectors. This paper analyzes the structure of orderings corresponding to larginal vectors of the core cover and conditions ensuring equality between core cover and core. We introduce compromise complete (or c-complete) sets that satisfy the condition that if every larginal vector corresponding to an ordering of the set is a core element, then the game is compromise stable. We use combinatorial arguments to give a complete characterization of these sets. More specifically, we find c-complete sets of minimum cardinality and a closed formula for the minimum number of orderings in c-complete sets.

Suggested Citation

  • Platz, Trine Tornøe & Hamers, Herbert & Quant, Marieke, 2012. "C-complete sets for compromise stable games," Discussion Papers of Business and Economics 25/2012, University of Southern Denmark, Department of Business and Economics.
  • Handle: RePEc:hhs:sdueko:2012_025

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    References listed on IDEAS

    1. Muto, S. & Nakayama, M. & Potters, J.A.M. & Tijs, S.H., 1988. "On big boss games," Other publications TiSEM 488a314a-179c-4628-91e6-7, Tilburg University, School of Economics and Management.
    2. Rafels, Carles & Ybern, Neus, 1995. "Even and Odd Marginal Worth Vectors, Owen's Multilinear Extension and Convex Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 113-126.
    3. repec:spr:compst:v:76:y:2012:i:3:p:343-359 is not listed on IDEAS
    4. Marieke Quant & Peter Borm & Hans Reijnierse & Bas van Velzen, 2005. "The core cover in relation to the nucleolus and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 491-503, November.
    5. van Velzen, S. & Hamers, H.J.M. & Norde, H.W., 2002. "Convexity and Marginal Vectors," Discussion Paper 2002-53, Tilburg University, Center for Economic Research.
    6. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
    7. A. Estévez-Fernández & M. Fiestras-Janeiro & M. Mosquera & E. Sánchez-Rodríguez, 2012. "A bankruptcy approach to the core cover," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 343-359, December.
    8. 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.
    9. 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.
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    Core; core cover; larginal vectors;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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