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The airport problem with capacity constraints

Author

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  • Youngsub Chun

    (Seoul National University)

  • Boram Park

    (Ajou University)

Abstract

The original airport problem is concerned with the cost sharing of an airstrip among airplanes assuming that one airstrip is sufficient to serve all airplanes. In this paper, we generalize the original airport problem by imposing capacity constraints to consider the situation when one airstrip cannot serve all airplanes and investigate how to share the cost among airplanes. We introduce the sequential equal contributions rule for our problem and show that it coincides with the Shapley value of the corresponding airport game when the worth of a coalition is defined to be the minimum cost of serving all members of the coalition. The sequential equal contributions rule requires each airplane to contribute equally to the cost of a given section of any airstrip as long as the length of the section is less than or equal to its desired length even though the airplane cannot use the airstrip. Each airplane’s contribution is the sum of terms, one for each section of the airstrip whose length is less than or equal to its desired length. We also present an axiomatic characterization of the rule by imposing the axioms of efficiency, the equal share lower bound, smaller-cost monotonicity, and population fairness.

Suggested Citation

  • Youngsub Chun & Boram Park, 2016. "The airport problem with capacity constraints," Review of Economic Design, Springer;Society for Economic Design, vol. 20(3), pages 237-253, September.
    • Handle: RePEc:spr:reecde:v:20:y:2016:i:3:d:10.1007_s10058-016-0191-3
    DOI: 10.1007/s10058-016-0191-3
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    References listed on IDEAS

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    1. Jean J. M. Derks & Hans H. Haller, 1999. "Null Players Out? Linear Values For Games With Variable Supports," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 301-314.
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    4. 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.
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    Cited by:

    1. Thomson, William, 2024. "Cost allocation and airport problems," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 17-31.

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    More about this item

    Keywords

    Airport problems with capacity constraints; Sequential equal contributions rule; Shapley value; Axiomatic characterization;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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