Symmetries of Quasi-Values

  • Ales A. Kubena
  • Peter Franek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8146)

Abstract

According to Shapley’s game-theoretical result, there exists a unique game value of finite cooperative games that satisfies axioms on additivity, efficiency, null-player property and symmetry. The original setting requires symmetry with respect to arbitrary permutations of players. We analyze the consequences of weakening the symmetry axioms and study quasi-values that are symmetric with respect to permutations from a  group G ≤ Sn. We classify all the permutation groups G that are large enough to assure a unique G-symmetric quasi-value, as well as the structure and dimension of the space of all such quasi-values for a general permutation group G.

We show how to construct G-symmetric quasi-values algorithmically by averaging certain basic quasi-values (marginal operators).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ales A. Kubena
    • 1
  • Peter Franek
    • 2
  1. 1.Institute of Information Theory and Automation of the ASCRPragueCzech Republic
  2. 2.Institute of Information TechnologiesCzech Technical UniversityPragueCzech Republic

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