Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations

Takayuki Oishi, Mikio Nakayama, Toru Hokari, Yukihiko Funaki

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


In this paper, for each solution for TU games, we define its "dual" and "anti-dual". Then, we apply these notions to axioms: two axioms are (anti-)dual to each other if whenever a solution satisfies one of them, its (anti-)dual satisfies the other. It turns out that these definitions allow us not only to organize existing axiomatizations of various solutions but also to find new axiomatizations of some solutions. As an illustration, we show that two well-known axiomatizations of the core are essentially equivalent in the sense that one can be derived from the other, and derive new axiomatizations of the Shapley value and the Dutta-Ray solution.

Original languageEnglish
Pages (from-to)44-53
Number of pages10
JournalJournal of Mathematical Economics
Publication statusPublished - 2016 Mar 1


  • Anti-duality
  • Core
  • Duality
  • Dutta-Ray solution
  • Shapley value

ASJC Scopus subject areas

  • Economics and Econometrics
  • Applied Mathematics


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