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Duality and Anti-duality for Allocation Rules in Economic Problems I: An Axiomatic Analysis

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  • Takayuki Oishi

Abstract

We develop the notions of duality and anti-duality for axiomatic analysis of allocation rules. First, we show basic properties of duality and anti-duality for allocation rules. Next, using the notion of duality and axioms involved in axiomatizations of the Shapley rule for airport problems, we axiomatize the Shapley rule for bidding ring problems. Finally, using the notion of anti- duality and axioms involved in axiomatizations of the nucleolus for airport problems, we axiomatize the nucleolus rule for bidding ring problems. From the approach proposed, we may derive appropriate interpretations of axioms involved in axiomatizations of economic rules.

Suggested Citation

  • Takayuki Oishi, 2018. "Duality and Anti-duality for Allocation Rules in Economic Problems I: An Axiomatic Analysis," Discussion Papers 38, Meisei University, School of Economics.
    • Handle: RePEc:mei:wpaper:38
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    References listed on IDEAS

    as
    1. Oishi, Takayuki & Nakayama, Mikio & Hokari, Toru & Funaki, Yukihiko, 2016. "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 44-53.
    2. Yan-An Hwang & Chun-Hsien Yeh, 2012. "A characterization of the nucleolus without homogeneity in airport problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 355-364, February.
    3. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    4. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    5. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Youngsub Chun & Cheng‐Cheng Hu & Chun‐Hsien Yeh, 2012. "Characterizations of the sequential equal contributions rule for the airport problem," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 77-85, March.
    7. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    8. William Thomson, 2007. "Cost allocation and airport problems," RCER Working Papers 537, University of Rochester - Center for Economic Research (RCER).
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    More about this item

    Keywords

    duality; anti-duality; axiomatization; Shapley rules; nucleolus rules;
    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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