Scandinavian Working Papers in Economics

Discussion Papers on Economics,
University of Southern Denmark, Department of Economics

No 10/2011: The prenucleolus for games with communication structures

Anna B. Khmelnitskaya () and Peter Sudhölter ()
Additional contact information
Anna B. Khmelnitskaya: Faculty of Applied Mathematics, Postal: University of Twente, P.O. Box 217, 7500 AE Enshede, The Netherlands
Peter Sudhölter: Department of Business and Economics, Postal: University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark

Abstract: t is well-known that the prenucleolus on the class of TU games is characterized by singlevaluedness, covariance under strategic equivalence, anonymity, and the reduced game property. We show that the prenucleolus on the class of TU games restricted to the connected coalitions with respect to communication structures may be characterized by the same axioms and a stronger version of independence of non-connected coalitions requiring that the solution does not depend on the worth of any non-connected coalition. Similarly as in the classical case, it turns out that each of the five axioms is logically independent of the remaining axioms and that an infinite universe of potential players is necessary. Moreover, a suitable definition and characterization of a prekernel for games with communication structures is presented.

Keywords: TU game; solution concept; communication and conference structure; nucleolus

JEL-codes: C71

15 pages, December 10, 2011

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