Three-valued simple games

M. Musegaas*, Peter Borm, M. Quant

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)


In this paper we study three-valued simple games as a natural extension of simple games. We analyze to which extent well-known results on the core and the Shapley value for simple games can be extended to this new setting. To describe the core of a three-valued simple game we introduce (primary and secondary) vital players, in analogy to veto players for simple games. Moreover, it is seen that the transfer property of Dubey (1975) can still be used to characterize the Shapley value for three-valued simple games. We illustrate three-valued simple games and the corresponding Shapley value in a parliamentary bicameral system.
Original languageEnglish
Pages (from-to)201-224
JournalTheory and Decision
Issue number2
Publication statusPublished - Aug 2018


  • Cooperative games
  • Three-valued simple games
  • Core
  • Vital players
  • Shapley value
  • Transfer property


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