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On the impact of independence of irrelevant alternatives

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  • Peleg, Bezalel

    ()
    (Institute of Mathematics and Center for the Study of Rationality)

  • Sudhölter, Peter

    ()
    (Department of Business and Economics)

  • Zarzuelo, José M.

    ()
    (Faculty of Economics and Business Administration)

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 Department of Business and Economics, University of Southern Denmark in its series Discussion Papers of Business and Economics with number 6/2010.

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Length: 11 pages
Date of creation: 05 Oct 2010
Date of revision:
Handle: RePEc:hhs:sdueko:2010_006

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Postal: Department of Business and Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Phone: 65 50 32 33
Fax: 65 50 32 37
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Web page: http://www.sdu.dk/ivoe
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Keywords: NTU game; Shapley NTU value; positive smoothness;

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