Nonsymmetric values under Hart-Mass-Colell consistency

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Let f be a single valued solution for cooperative TU games that satisfies inessential game property, efficiency, Hart Mas-Colell consistency and for two person games is strictly monotonic and individually unbounded. Then there exists a family of strictly increasing functions associated with players that completely determines f. For two person games, both players have equal differences between their functions at the solution point and at the values of characteristic function of their singletons. This solution for two person games is uniquely extended to n person games due to consistency and efficiency. The extension uses the potential with respect to the family of functions and generalizes potentials introduced by Hart and Mas Colell [6]. The weighted Shapley values, the proportional value described by Ortmann [11], and new values generated by power functions are among these solutions.

Translated title of the contributionНесимметричные значения, удовлетворяющие согласованности по Харту-Мас-Колеллу
Original languageEnglish
Pages (from-to)523-534
Number of pages12
JournalInternational Journal of Game Theory
Issue number4
StatePublished - 1 Nov 2005

Scopus subject areas

  • Mathematics (miscellaneous)
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Decision Sciences(all)


  • Claim problem
  • Consistency
  • Potential
  • Shapley value


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