The banzhaf value and general semivalues for differentiable mixed games

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We consider semivalues on pM—a vector space of games with a continuum of players (among which there may be atoms) that possess a robust differentiability feature. We introduce the notion of a derivative semivalue on pM and extend the standard Banzhaf value from the domain of finite games onto pM as a certain particularly simple derivative semivalue. Our main result shows that any semivalue on pM is a derivative semivalue. It is also shown that the Banzhaf value is the only semivalue on pM that satisfies a version of the composition property of Owen and that, in addition, is nonzero for all nonzero monotonic finite games.

Original languageEnglish
Pages (from-to)767-782
Number of pages16
JournalMathematics of Operations Research
Issue number3
StatePublished - 1 Jan 2019


  • Banzhaf value
  • Composition property
  • Compound game
  • Continuum of players
  • Mixed games
  • Nonatomic games
  • Semivalues

ASJC Scopus subject areas

  • General Mathematics
  • Computer Science Applications
  • Management Science and Operations Research


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