Set Functions, Capacities and Games

  • Michel Grabisch
Part of the Theory and Decision Library C book series (TDLC, volume 46)


This chapter opens the fundamental part of the book, focusing on mathematical properties. It presents the main classes of set functions that will be considered throughout the book, namely games (set functions vanishing on the empty set) and capacities (monotone games). In the main part of this chapter (Sects. 2.1– 2.18), we consider set functions defined on a nonempty finite set X, where the domain of set functions is the power set 2 X . In Sect. 2.19 we briefly address the case of arbitrary spaces and domains.


Polynomial Representation Cooperative Game Theory Walsh Function Possibility Measure Linear Invertible 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Michel Grabisch
    • 1
  1. 1.Paris School of EconomicsUniversité Paris I Panthéon-SorbonneParisFrance

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