Abstract
On several classes of n-person NTU games that have at least one Shapley NTU value, Aumann characterized this solution by six axioms: Non-emptiness, efficiency, unanimity, scale covariance, conditional additivity, and independence of irrelevant alternatives (IIA). Each of the first five axioms is logically independent of the remaining axioms, and the logical independence of IIA is an open problem. We show that for n = 2 the first five axioms already characterize the Shapley NTU value, provided that the class of games is not further restricted. Moreover, we present an example of a solution that satisfies the first five axioms and violates IIA for two-person NTU games (N, V) with uniformly p-smooth V(N).
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We are grateful to two anonymous referees of this journal for their comments that helped to improve the writing of this paper. The second and third author were supported by the Spanish Ministerio de Ciencia e Innovación under project ECO2009-11213, co-funded by the ERDF.
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Peleg, B., Sudhölter, P. & Zarzuelo, J.M. On the impact of independence of irrelevant alternatives: the case of two-person NTU games. SERIEs 3, 143–156 (2012). https://doi.org/10.1007/s13209-011-0043-x
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DOI: https://doi.org/10.1007/s13209-011-0043-x