Scandinavian Working Papers in Economics

Discussion Papers of Business and Economics,
University of Southern Denmark, Department of Business and Economics

No 4/2012: On extensions of the core and the anticore of transferable utility games

Jean Derks (), Hans Peters () and Peter Sudhölter ()
Additional contact information
Jean Derks: Department of Knowledge Engineering, Postal: Maastricht University, The Netherlands
Hans Peters: Department of Quantitative Economics, Postal: Maastricht University, The Netherlands
Peter Sudhölter: Department of Business and Economics, Postal: University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

Abstract: We 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.

Keywords: Transferable utility game; core; anticore; core extension; min-prenucleolus

JEL-codes: C71

28 pages, January 6, 2012

Full text files

%7BCDEE1F10-DE3D-4D56-B444-F27EF25FB232%7Ddpbe4_2012.pdf PDF-file 

Download statistics

Questions (including download problems) about the papers in this series should be directed to Lene Holbæk ()
Report other problems with accessing this service to Sune Karlsson ().

This page generated on 2018-01-23 23:37:40.