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On the impact of independence of irrelevant alternatives

Author

Listed:
  • 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).

Suggested Citation

  • Peleg, Bezalel & Sudhölter, Peter & Zarzuelo, José M., 2010. "On the impact of independence of irrelevant alternatives," Discussion Papers on Economics 6/2010, University of Southern Denmark, Department of Economics.
    • Handle: RePEc:hhs:sdueko:2010_006
    as

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    References listed on IDEAS

    as
    1. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    2. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, December.
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    More about this item

    Keywords

    NTU game; Shapley NTU value; positive smoothness;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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