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C-complete sets for compromise stable games

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  • Platz, Trine Tornøe

    ()
    (Department of Business and Economics)

  • Hamers, Herbert

    ()
    (Department of Econometrics & OR and CentER)

  • Quant, Marieke

    (Department of Econometrics & OR and CentER)

Abstract

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.

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Bibliographic Info

Paper provided by Department of Business and Economics, University of Southern Denmark in its series Discussion Papers of Business and Economics with number 25/2012.

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Length: 14 pages
Date of creation: 03 Dec 2012
Date of revision:
Handle: RePEc:hhs:sdueko:2012_025

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Postal: Department of Business and Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Phone: 65 50 32 33
Fax: 65 50 32 37
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Web page: http://www.sdu.dk/ivoe
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Keywords: Core; core cover; larginal vectors;

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  1. 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.
  2. Tijs, S.H. & Lipperts, F.A.S., 1982. "The hypercube and the core cover of N-person cooperative games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154285, Tilburg University.
  3. 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.
  4. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, Elsevier, vol. 1(3), pages 275-293, September.
  5. Velzen, S. van & Hamers, H.J.M. & Norde, H.W., 2002. "Convexity and Marginal Vectors," Discussion Paper, Tilburg University, Center for Economic Research 2002-53, Tilburg University, Center for Economic Research.
  6. Rafels, Carles & Ybern, Neus, 1995. "Even and Odd Marginal Worth Vectors, Owen's Multilinear Extension and Convex Games," International Journal of Game Theory, Springer, Springer, vol. 24(2), pages 113-26.
  7. Velzen, S. van & Hamers, H.J.M. & Norde, H.W., 2003. "Characterizing Convexity of Games using Marginal Vectors," Discussion Paper, Tilburg University, Center for Economic Research 2003-11, Tilburg University, Center for Economic Research.
  8. 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.
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