Shapley mappings and the cumulative value for n-person games with fuzzy coalitions

Dan Butnariu, Tomáš Kroupa

Research output: Contribution to journalArticlepeer-review


In this paper we prove existence and uniqueness of the so-called Shapley mapping, which is a solution concept for a class of n-person games with fuzzy coalitions whose elements are defined by the specific structure of their characteristic functions. The Shapley mapping, when it exists, associates to each fuzzy coalition in the game an allocation of the coalitional worth satisfying the efficiency, the symmetry, and the null-player conditions. It determines a "cumulative value" that is the "sum" of all coalitional allocations for whose computation we provide an explicit formula.

Original languageEnglish
Pages (from-to)288-299
Number of pages12
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - 1 Apr 2008


  • Coalition
  • Cumulative value
  • Fuzzy coalition
  • n-Person cooperative game
  • Shapley value

ASJC Scopus subject areas

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management
  • Industrial and Manufacturing Engineering


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