Abstract
It is well-known that the prekernel on the class of TU games is uniquely determined by non-emptiness, Pareto efficiency (EFF), covariance under strategic equivalence (COV), the equal treatment property, the reduced game property (RGP), and its converse. We show that the prekernel on the class of TU games restricted to the connected coalitions with respect to communication structures may be axiomatized by suitably generalized axioms. Moreover, it is shown that the prenucleolus, the unique solution concept on the class of TU games that satisfies singlevaluedness, COV, anonymity, and RGP, may be characterized by suitably generalized versions of these axioms together with a property that is called “independence of irrelevant connections”. This property requires that any element of the solution to a game with communication structure is an element of the solution to the game that allows unrestricted cooperation in all connected components, provided that each newly connected coalition is sufficiently charged, i.e., receives a sufficiently small worth. Both characterization results may be extended to games with conference structures.
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We are grateful to José M. Zarzuelo for his constructive comments and to an anonymous referee for comments that helped to improve the writing of this paper. The first author thanks the Instituto de Matemática Interdisciplinar (IMI) for a research grant enabling to work in 2011 at Complutense University of Madrid, in particular, on this topic. Her research on the paper was also partially done during her research stay at the University of Twente the hospitality of which she much appreciates. The University of Twente granted a one weak research stay to the second author, who was also supported by the Spanish Ministerio de Ciencia e Innovación under the projects ECO2009-11213 and ECO2012-33618, co-funded by the ERDF and by the Danish Council for Independent Research | Social Sciences under the FINQ project.
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Khmelnitskaya, A., Sudhölter, P. The prenucleolus and the prekernel for games with communication structures. Math Meth Oper Res 78, 285–299 (2013). https://doi.org/10.1007/s00186-013-0444-7
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DOI: https://doi.org/10.1007/s00186-013-0444-7