On extensions of the core and the anticore of transferable utility games
We consider several related set extensions of the core and the anticore of games with transferableutility. An efficient allocation is undominated if it cannot be improved, in a specific way, bysidepayments changing the allocation or the game. The set of all such allocations is called theundominated set, and we show that it consists of finitely many polytopes with a core-likestructure. One of these polytopes is the L1-center, consisting of all efficient allocations thatminimize the sum of the absolute values of the excesses. Theexcess Pareto optimal set contains the allocations that are Pareto optimal in the set obtained byordering the sums of the absolute values of the excesses of coalitions and the absolute values ofthe excesses of their complements. The L1-center is contained in the excess Pareto optimal set,which in turn is contained in the undominated set. For three-person games all these sets coincide.These three sets also coincide with the core for balanced games and with the anticore forantibalanced games. We study properties of these sets and provide characterizations in terms ofbalanced collections of coalitions. We also propose a single-valued selection from the excessPareto optimal set, the min-prenucleolus, which is defined as the prenucleolus ofthe minimum of a game and its dual.
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- Bossert, Walter & Derks, Jean & Peters, Hans, 2005.
"Efficiency in uncertain cooperative games,"
Mathematical Social Sciences,
Elsevier, vol. 50(1), pages 12-23, July.
- Bossert,Walter & Derks,Jean & Peters,Hans, 2001. "Efficiency in Uncertain Cooperative Games," Research Memorandum 002, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- BOSSERT, Walter & DERKS, Jean & PETERS, Hans, 2001. "Efficiency in Uncertain Cooperative Games," Cahiers de recherche 2001-14, Universite de Montreal, Departement de sciences economiques.
- Bossert, W. & Derks, J. & Peters, H., 2001. "Efficiency in Uncertain Cooperative Games," Cahiers de recherche 2001-14, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Derks, Jean & Peters, Hans, 1998. "Orderings, excess functions, and the nucleolus," Mathematical Social Sciences, Elsevier, vol. 36(2), pages 175-182, September.
- Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 187-200.
- Guni Orshan & Peter Sudhölter, 2010. "The positive core of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 113-136, March.
- Camelia Bejan & Juan Gómez, 2009. "Core extensions for non-balanced TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(1), pages 3-16, March. Full references (including those not matched with items on IDEAS)