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 Department of Business and Economics, University of Southern Denmark in its series Discussion Papers of Business and Economics with number 6/2010.
Length: 11 pages
Date of creation: 05 Oct 2010
Date of revision:
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NTU game; Shapley NTU value; positive smoothness;
Other versions of this item:
- Bezalel Peleg & Peter Sudholter & Jose M. Zarzuelo, 2010. "On the Impact of Independence of Irrelevant Alternatives," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp561, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-07-13 (All new papers)
- NEP-GTH-2011-07-13 (Game Theory)
- NEP-MIC-2011-07-13 (Microeconomics)
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- Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, Econometric Society, vol. 18(2), pages 155-162, April.
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