On the impact of independence of irrelevant alternatives
Bezalel Peleg (),
Peter Sudhölter () and
José M. Zarzuelo ()
Additional contact information José M. Zarzuelo: Faculty of Economics and Business Administration, Postal: Basque Country University, Lehendakari Aguirre 83, 48015 Bilbao, Spain
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).