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A General Derivation of Axiomatizations for Allocation Rules: Duality and Anti-Duality Approach

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  • Takayuki Oishi

    (Faculty of Economics, Meisei University)

Abstract

We offer a general derivation of axiomatizations for allocation rules, referred to as "duality" and "anti-duality" approach. We show basic properties of duality and antiduality approach. Using these properties, we can derive axiomatizations of allocation rules by taking (anti-)dual of axioms involved in axiomatizations of their self-(anti-)dual rules. As an illustration, we derive a new axiomatization of the Shapley value for bidding ring problems from using the notion of duality and axioms involved in axiomatizations of the Shapley value for airport problems. As another illustration, we derive a new axiomatization of the nucleolus for bidding ring problems from using the notion of antiduality and axioms involved in axiomatizations of the nucleolus for airport problems.

Suggested Citation

  • Takayuki Oishi, 2019. "A General Derivation of Axiomatizations for Allocation Rules: Duality and Anti-Duality Approach," Keio-IES Discussion Paper Series 2019-011, Institute for Economics Studies, Keio University.
    • Handle: RePEc:keo:dpaper:2019-011
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    References listed on IDEAS

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    1. Potters, Jos & Sudholter, Peter, 1999. "Airport problems and consistent allocation rules," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 83-102, July.
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    More about this item

    Keywords

    duality; anti-duality; axiomatization; Shapley value; nucleolus;
    All these keywords.

    JEL classification:

    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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