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On the Impact of Independence of Irrelevant Alternatives

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  • Bezalel Peleg
  • Peter Sudholter
  • Jose M. Zarzuelo

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).

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp561.

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Length: 12 pages
Date of creation: Oct 2010
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Publication status: 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"
Handle: RePEc:huj:dispap:dp561

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  1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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