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Stable sets and max-convex decompositions of TU games

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  • Francesc Llerena
  • Carles Rafels

Abstract

We study under which conditions the core of a game involved in a max-convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas’ five player game with a unique stable set different from the core, are reckoning and analyzed. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • Francesc Llerena & Carles Rafels, 2013. "Stable sets and max-convex decompositions of TU games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(2), pages 313-322, July.
    • Handle: RePEc:spr:topjnl:v:21:y:2013:i:2:p:313-322
    DOI: 10.1007/s11750-011-0177-9
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    References listed on IDEAS

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    1. F. Javier Martínez-de-Albéniz & Carles Rafels, 2004. "An intersection theorem in TU cooperative game theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 107-114, January.
    2. Llerena, Francesc & Rafels, Carles, 2006. "The vector lattice structure of the n-person TU games," Games and Economic Behavior, Elsevier, vol. 54(2), pages 373-379, February.
    3. Einy, Ezra, 1988. "The shapley value on some lattices of monotonic games," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 1-10, February.
    4. Rafels, C. & Tijs, S.H., 1997. "On the cores of cooperative games and the stability of the Weber set," Other publications TiSEM 14435da8-14ce-4845-8e54-4, Tilburg University, School of Economics and Management.
    5. Lucas, William F., 1992. "Von Neumann-Morgenstern stable sets," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 17, pages 543-590, Elsevier.
    6. 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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    Keywords

    Coalitional games; Convex games; Stable sets; Core; 91A12;
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