Self-antidual extensions and subsolutions

Bas Dietzenbacher and Elena Yanovskaya

Mathematical Social Sciences, 2021, vol. 114, issue C, 105-109

Abstract: 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.

Keywords: transferable utility games; antiduality; minimal self-antidual extension; maximal self-antidual subsolution (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:114:y:2021:i:c:p:105-109

DOI: 10.1016/j.mathsocsci.2021.08.004

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