On extensions of the core and the anticore of transferable utility games
AbstractWe consider several related set extensions of the core and the anticore of games with transferable utility. An efficient allocation is undominated if it cannot be improved, in a specific way, by sidepayments changing the allocation or the game. The set of all such allocations is called the undominated set, and we show that it consists of finitely many polytopes with a core-like structure. One of these polytopes is the L1-center, consisting of all efficient allocations that minimize the sum of the absolute values of the excesses. The excess Pareto optimal set contains the allocations that are Pareto optimal in the set obtained by ordering the sums of the absolute values of the excesses of coalitions and the absolute values of the 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 for antibalanced games. We study properties of these sets and provide characterizations in terms of balanced collections of coalitions. We also propose a single-valued selection from the excess Pareto optimal set, the min-prenucleolus, which is defined as the prenucleolus of the minimum of a game and its dual.
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Bibliographic InfoPaper provided by Department of Business and Economics, University of Southern Denmark in its series Discussion Papers of Business and Economics with number 4/2012.
Length: 28 pages
Date of creation: 06 Jan 2012
Date of revision:
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Transferable utility game; core; anticore; core extension; min-prenucleolus;
Other versions of this item:
- Jean Derks & Hans Peters & Peter Sudhölter, 2014. "On extensions of the core and the anticore of transferable utility games," International Journal of Game Theory, Springer, vol. 43(1), pages 37-63, February.
- Derks Jean & Peters Hans & Sudhölter Peter, 2012. "On extensions of the core and the anticore of transferable utility games," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-02-08 (All new papers)
- NEP-CDM-2012-02-08 (Collective Decision-Making)
- NEP-GTH-2012-02-08 (Game Theory)
- NEP-MIC-2012-02-08 (Microeconomics)
- NEP-UPT-2012-02-08 (Utility Models & Prospect Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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).
- Guni Orshan & Peter Sudhölter, 2010.
"The positive core of a cooperative game,"
International Journal of Game Theory,
Springer, vol. 39(1), pages 113-136, March.
- Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
- Camelia Bejan & Juan Gómez, 2009. "Core extensions for non-balanced TU-games," International Journal of Game Theory, Springer, vol. 38(1), pages 3-16, March.
- Derks, Jean & Peters, Hans, 1998. "Orderings, excess functions, and the nucleolus," Mathematical Social Sciences, Elsevier, vol. 36(2), pages 175-182, September.
- Michel Grabisch & Peter Sudhölter, 2014.
"The positive core for games with precedence constraints,"
Documents de travail du Centre d'Economie de la Sorbonne
14036, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
- Grabisch, Michel & Sudhölter, Peter, 2014. "The positive core for games with precedence constraints," Discussion Papers of Business and Economics 8/2014, Department of Business and Economics, University of Southern Denmark.
- Alexander Karpov, 2012. "Equal Weights Coauthorship Sharing and Shapley Value are Equivalen," HSE Working papers WP BRP 03/STI/2012, National Research University Higher School of Economics.
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