Self-antidual extensions and subsolutions

Bas Dietzenbacher*, Elena Yanovskaya*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


A solution for transferable utility games is self-antidual if it assigns to each game the set of payoff allocations that it assigns to the antidual game with opposite sign. Well-known examples of self-antidual solutions are the core, the Shapley value, the prenucleolus, and the Dutta–Ray solution. To evaluate the extent to which a solution violates self-antiduality, this note defines its minimal self-antidual extension, i.e. the smallest self-antidual solution that contains it. Similarly, the maximal self-antidual subsolution is defined, i.e. the largest self-antidual solution that the solution contains. We show that both the minimal self-antidual extension and the maximal self-antidual subsolution uniquely exist for each solution. As an application, we study self-antiduality of the imputations solution.
Original languageEnglish
Pages (from-to)105-109
Number of pages5
JournalMathematical Social Sciences
Publication statusPublished - Nov 2021


  • transferable utility games
  • antiduality
  • minimal self-antidual extension
  • maximal self-antidual subsolution


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