Scandinavian Working Papers in Economics

Discussion Papers on Economics,
University of Southern Denmark, Department of Economics

No 6/2010: On the impact of independence of irrelevant alternatives

Bezalel Peleg (), Peter Sudhölter () and José M. Zarzuelo ()
Additional contact information
Bezalel Peleg: Institute of Mathematics and Center for the Study of Rationality, Postal: The Hebrew University of Jerusalem, Feldman Building, Givat Ram, 91904 Jerusalem, Israel
Peter Sudhölter: Department of Business and Economics, Postal: University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
José M. Zarzuelo: Faculty of Economics and Business Administration, Postal: Basque Country University, Lehendakari Aguirre 83, 48015 Bilbao, Spain

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).

Keywords: NTU game; Shapley NTU value; positive smoothness

JEL-codes: C71

11 pages, October 5, 2010

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