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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 ≤ S n . 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).

Keywords

Cooperative Game Permutation Group Marginal Operator Cooperative Game Theory Cycle Index 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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