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 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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Bibliographic InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 003.
Date of creation: 2012
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Other versions of this item:
- Derks, Jean & Peters, Hans & Sudhölter, Peter, 2012. "On extensions of the core and the anticore of transferable utility games," Discussion Papers of Business and Economics 4/2012, Department of Business and Economics, University of Southern Denmark.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-03 (All new papers)
- NEP-CDM-2012-09-03 (Collective Decision-Making)
- NEP-GTH-2012-09-03 (Game Theory)
- NEP-MIC-2012-09-03 (Microeconomics)
- NEP-UPT-2012-09-03 (Utility Models & Prospect Theory)
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