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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Postal: Department of Business and Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
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Transferable utility game; core; anticore; core extension; min-prenucleolus;
Other versions of this item:
- Derks Jean & Peters Hans & Sudhölter Peter, 2012. "On extensions of the core and the anticore of transferable utility games," Research Memoranda 003, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
- 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)
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- 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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