Mathematical Methods of Operations Research

, Volume 78, Issue 2, pp 285–299 | Cite as

The prenucleolus and the prekernel for games with communication structures

  • Anna Khmelnitskaya
  • Peter Sudhölter
Original Article


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.


TU game Solution concept Communication and conference structure Nucleolus Kernel 

JEL Classification



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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of Applied MathematicsSaint-Petersburg State UniversitySaint-PetersburgRussia
  2. 2.Department of Business and Economics, COHEREUniversity of Southern DenmarkOdense MDenmark

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