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On the Impact of Independence of Irrelevant Alternatives

Bezalel Peleg, Peter Sudhölter () and José Zarzuelo ()

Discussion Paper Series from The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem

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 5 axioms and violates IIA for 2-person NTU games (N;V) with uniformly p-smooth V(N).

Pages: 12 pages
Date: 2010-10
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Published in SERIEs (the Journal of the Spanish Economic Association) (2012) 3:143-156 under the longer title: "On the impact of independence of irrelevant alternatives: the case of two-person NTU games"

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Working Paper: On the impact of independence of irrelevant alternatives (2010) Downloads
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