On the Impact of Independence of Irrelevant Alternatives
AbstractOn 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 InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp561.
Length: 12 pages
Date of creation: Oct 2010
Date of revision:
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"
Other versions of this item:
- Peleg, Bezalel & Sudhölter, Peter & Zarzuelo, José M., 2010. "On the impact of independence of irrelevant alternatives," Discussion Papers of Business and Economics 6/2010, Department of Business and Economics, University of Southern Denmark.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
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