IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v131y2024icp17-31.html
   My bibliography  Save this article

Cost allocation and airport problems

Author

Listed:
  • Thomson, William

Abstract

We consider the problem of dividing the cost of a facility when agents can be ordered in terms of the needs they have for it, and accommodating an agent with a certain need allows accommodating all agents with lower needs at no extra cost. This problem is known as the “airport problem”, the facility being the runway. We review the literature devoted to its study, and formulate a number of open questions.

Suggested Citation

  • Thomson, William, 2024. "Cost allocation and airport problems," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 17-31.
    • Handle: RePEc:eee:matsoc:v:131:y:2024:i:c:p:17-31
    DOI: 10.1016/j.mathsocsci.2024.03.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489624000386
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2024.03.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. H. Peyton Young, 1987. "On Dividing an Amount According to Individual Claims or Liabilities," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 398-414, August.
    2. Dutta, Bhaskar & Ray, Debraj, 1989. "A Concept of Egalitarianism under Participation Constraints," Econometrica, Econometric Society, vol. 57(3), pages 615-635, May.
    3. Chun, Youngsub & Thomson, William, 2005. "Convergence under replication of rules to adjudicate conflicting claims," Games and Economic Behavior, Elsevier, vol. 50(2), pages 129-142, February.
    4. 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.
    5. Kolpin, Van, 1998. "Equitable Nonlinear Price Regulation: An Alternative Approach to Serial Cost Sharing," Games and Economic Behavior, Elsevier, vol. 22(1), pages 61-83, January.
    6. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    7. Julio González-Díaz & Miguel Mirás Calvo & Carmen Sandomingo & Estela Rodríguez, 2015. "Monotonicity of the core-center of the airport game," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 773-798, October.
    8. J. Arin & E. Inarra & P. Luquin, 2009. "A noncooperative view on two airport cost sharing rules," Review of Economic Design, Springer;Society for Economic Design, vol. 13(4), pages 361-376, December.
    9. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    10. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2012. "Axiomatic and strategic justifications for the constrained equal benefits rule in the airport problem," Games and Economic Behavior, Elsevier, vol. 75(1), pages 185-197.
    11. Youngsub Chun & Cheng-Cheng Hu & Chun-Hsien Yeh, 2017. "A Strategic Implementation of the Shapley Value for the Nested Cost-Sharing Problem," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 19(1), pages 219-233, February.
    12. Julio González-Díaz & Estela Sánchez-Rodríguez, 2007. "A natural selection from the core of a TU game: the core-center," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 27-46, September.
    13. William Thomson, 1983. "The Fair Division of a Fixed Supply Among a Growing Population," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 319-326, August.
    14. Bergantinos, Gustavo & Vidal-Puga, Juan J., 2007. "A fair rule in minimum cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 326-352, November.
    15. Dutta, Bhaskar & Kar, Anirban, 2004. "Cost monotonicity, consistency and minimum cost spanning tree games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 223-248, August.
    16. Toyotaka Sakai, 2012. "Fair waste pricing: an axiomatic analysis to the NIMBY problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(2), pages 499-521, June.
    17. Rodica Brânzei & Elena Iñarra & Stef Tijs & José Zarzuelo, 2006. "A Simple Algorithm for the Nucleolus of Airport Profit Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 259-272, August.
    18. Schummer, James & Thomson, William, 1997. "Two derivations of the uniform rule and an application to bankruptcy," Economics Letters, Elsevier, vol. 55(3), pages 333-337, September.
    19. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-1037, September.
    20. 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.
    21. Márkus, Judit & Pintér, Miklós & Radványi, Anna, 2011. "The Shapley value for airport and irrigation games," MPRA Paper 30031, University Library of Munich, Germany.
    22. Casas-Mendez, Balbina & Garcia-Jurado, Ignacio & van den Nouweland, Anne & Vazquez-Brage, Margarita, 2003. "An extension of the [tau]-value to games with coalition structures," European Journal of Operational Research, Elsevier, vol. 148(3), pages 494-513, August.
    23. 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.
    24. 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.
    25. Aadland, David & Kolpin, Van, 1998. "Shared irrigation costs: An empirical and axiomatic analysis," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 203-218, March.
    26. S.C. Littlechild & G.F. Thompson, 1977. "Aircraft Landing Fees: A Game Theory Approach," Bell Journal of Economics, The RAND Corporation, vol. 8(1), pages 186-204, Spring.
    27. M. Albizuri & J. Echarri & J. Zarzuelo, 2015. "A non-cooperative mechanism for the Shapley value of airport problems," Annals of Operations Research, Springer, vol. 235(1), pages 1-11, December.
    28. 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.
    29. William Thomson, 2023. "The Axiomatics of Economic Design, Vol. 1," Studies in Choice and Welfare, Springer, number 978-3-031-29398-6, June.
    30. S. H. Tijs & M. Koster & E. Molina & Y. Sprumont, 2002. "Sharing the cost of a network: core and core allocations," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 567-599.
    31. S. Z. Alparslan Gök, 2012. "On the Interval Baker-Thompson Rule," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-5, May.
    32. Michael Maschler & Jos Potters & Hans Reijnierse, 2010. "The nucleolus of a standard tree game revisited: a study of its monotonicity and computational properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 89-104, March.
    33. William Thomson, 2023. "Complements to the Axiomatic Method in Economic Design," Studies in Choice and Welfare, in: The Axiomatics of Economic Design, Vol. 1, chapter 0, pages 269-285, Springer.
    34. González-Díaz, Julio & Mirás Calvo, Miguel Ángel & Quinteiro Sandomingo, Carmen & Sánchez Rodríguez, Estela, 2016. "Airport games: The core and its center," Mathematical Social Sciences, Elsevier, vol. 82(C), pages 105-115.
    35. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2018. "A study of the nucleolus in the nested cost-sharing problem: Axiomatic and strategic perspectives," Games and Economic Behavior, Elsevier, vol. 109(C), pages 82-98.
    36. Pradeep Dubey, 1982. "The Shapley Value as Aircraft Landing Fees--Revisited," Management Science, INFORMS, vol. 28(8), pages 869-874, August.
    37. Hou, Dongshuang & Sun, Hao & Sun, Panfei & Driessen, Theo, 2018. "A note on the Shapley value for airport cost pooling game," Games and Economic Behavior, Elsevier, vol. 108(C), pages 162-169.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sanchez-Soriano, Joaquin, 2021. "Families of sequential priority rules and random arrival rules with withdrawal limits," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 136-148.
    2. Hu, Cheng-Cheng & Tsay, Min-Hung & Yeh, Chun-Hsien, 2018. "A study of the nucleolus in the nested cost-sharing problem: Axiomatic and strategic perspectives," Games and Economic Behavior, Elsevier, vol. 109(C), pages 82-98.
    3. Hougaard, Jens Leth & Tvede, Mich & Østerdal, Lars Peter, 2013. "Cost Sharing in Chains and Other Fixed Trees," Discussion Papers on Economics 12/2013, University of Southern Denmark, Department of Economics.
    4. Márkus, Judit & Pintér, Miklós & Radványi, Anna, 2011. "The Shapley value for airport and irrigation games," MPRA Paper 30031, University Library of Munich, Germany.
    5. 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.
    6. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
    7. Juan D. Moreno-Ternero & Min-Hung Tsay & Chun-Hsien Yeh, 2020. "A strategic justification of the Talmud rule based on lower and upper bounds," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1045-1057, December.
    8. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    9. Grahame F. Thompson, 2020. "Deal or no deal? Some reflections on the ‘Baker-Thompson rule,’ ‘matching,’ and ‘market design’," Journal of Cultural Economy, Taylor & Francis Journals, vol. 13(5), pages 652-662, September.
    10. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    11. Alcalde-Unzu, Jorge & Gallo, Oihane & Inarra, Elena & Moreno-Ternero, Juan D., 2024. "Solidarity to achieve stability," European Journal of Operational Research, Elsevier, vol. 315(1), pages 368-377.
    12. Fatemeh Babaei & Hamidreza Navidi & Stefano Moretti, 2022. "A bankruptcy approach to solve the fixed cost allocation problem in transport systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 332-358, July.
    13. Chun, Y. & Kayi, C. & Yeh, C.-H., 2008. "Consistency and the sequential equal contributions rule for airport problems," Research Memorandum 039, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    14. Tamas Solymosi & Balazs Sziklai, 2015. "Universal Characterization Sets for the Nucleolus in Balanced Games," CERS-IE WORKING PAPERS 1512, Institute of Economics, Centre for Economic and Regional Studies.
    15. Paula Jaramillo, 2013. "Congestion in irrigation problems," Documentos CEDE 10553, Universidad de los Andes, Facultad de Economía, CEDE.
    16. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Tvede, Mich & Østerdal, Lars Peter, 2017. "Sharing the proceeds from a hierarchical venture," Games and Economic Behavior, Elsevier, vol. 102(C), pages 98-110.
    17. Sylvain Béal & Adriana Navarro-Ramos & Eric Rémila & Philippe Solal, 2023. "Sharing the cost of hazardous transportation networks and the Priority Shapley value," Working Papers hal-04222245, HAL.
    18. Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez Rodríguez, 2016. "Monotonicity implications for the ranking of rules for airport problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 379-400, December.
    19. Flores-Szwagrzak, Karol & Østerdal, Lars Peter, 2024. "Rationalizing Sharing Rules," Working Papers 17-2024, Copenhagen Business School, Department of Economics.
    20. Zou, Zhengxing & van den Brink, René & Funaki, Yukihiko, 2021. "Compromising between the proportional and equal division values," Journal of Mathematical Economics, Elsevier, vol. 97(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:131:y:2024:i:c:p:17-31. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.