IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v82y2016icp105-115.html
   My bibliography  Save this article

Airport games: The core and its center

Author

Listed:
  • González-Díaz, Julio
  • Mirás Calvo, Miguel Ángel
  • Quinteiro Sandomingo, Carmen
  • Sánchez Rodríguez, Estela

Abstract

An approach to define a rule for an airport problem is to associate to each problem a cooperative game, an airport game, and using game theory to come out with a solution. In this paper, we study the rule that is the average of all the core allocations: the core-center (González-Díaz and Sánchez-Rodríguez, 2007). The structure of the core is exploited to derive insights on the core-center. First, we provide a decomposition of the core in terms of the cores of the downstream-subtraction reduced games. Then, we analyze the structure of the faces of the core of an airport game that correspond to the no-subsidy constraints to find that the faces of the core can be seen as new airport games, the face games, and that the core can be decomposed through the no-subsidy cones (those whose bases are the cores of the no-subsidy face games). As a consequence, we provide two methods for computing the core-center of an airport problem, both with interesting economic interpretations: one expresses the core-center as a ratio of the volume of the core of an airport game for which a player is cloned over the volume of the original core, the other defines a recursive algorithm to compute the core-center through the no-subsidy cones. Finally, we prove that the core-center is not only an intuitive appealing game-theoretic solution for the airport problem but it has also a good behavior with respect to the basic properties one expects an airport rule to satisfy. We examine some differences between the core-center and, arguably, the two more popular game theoretic solutions for airport problems: the Shapley value and the nucleolus.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:matsoc:v:82:y:2016:i:c:p:105-115
    DOI: 10.1016/j.mathsocsci.2016.04.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489616300336
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.mathsocsci.2016.04.007?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. 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.
    2. 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.
    3. 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).
    4. 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.
    5. Thomson, William, 1988. "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, Elsevier, vol. 46(2), pages 237-254, December.
    6. Gerard Debreu, 1963. "On a Theorem of Scarf," Review of Economic Studies, Oxford University Press, vol. 30(3), pages 177-180.
    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. 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.
    2. Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2021. "Considerations on the aggregate monotonicity of the nucleolus and the core-center," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 291-325, April.
    3. Martin Shubik, 1984. "The Cooperative Form, the Value and the Allocation of Joint Costs and Benefits," Cowles Foundation Discussion Papers 706, Cowles Foundation for Research in Economics, Yale University.
    4. Nir Dagan, 1995. "Consistent Solutions in Exchange Economies: a Characterization of the Price Mechanism," Economic theory and game theory 011, Nir Dagan.
    5. 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.
    6. 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.
    7. García-Martínez, Jose A. & Mayor-Serra, Antonio J. & Meca, Ana, 2020. "Efficient Effort Equilibrium in Cooperation with Pairwise Cost Reduction," MPRA Paper 105604, University Library of Munich, Germany.
    8. Csóka, Péter & Illés, Ferenc & Solymosi, Tamás, 2022. "On the Shapley value of liability games," European Journal of Operational Research, Elsevier, vol. 300(1), pages 378-386.
    9. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2020. "Allocating extra revenues from broadcasting sports leagues," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 65-73.
    10. Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2022. "The average-of-awards rule for claims problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 863-888, November.
    11. J. Keith Murnighan & Alvin E. Roth, 1978. "Large Group Bargaining in a Characteristic Function Game," Journal of Conflict Resolution, Peace Science Society (International), vol. 22(2), pages 299-317, June.
    12. Dehez, Pierre & Ferey, Samuel, 2013. "How to share joint liability: A cooperative game approach," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 44-50.
    13. Pierre Dehez, 2013. "Cooperative provision of indivisible public goods," Theory and Decision, Springer, vol. 74(1), pages 13-29, January.
    14. Minyoung Yea & Seokhyun Chung & Taesu Cheong & Daeki Kim, 2018. "The Sharing of Benefits from a Logistics Alliance Based on a Hub-Spoke Network: A Cooperative Game Theoretic Approach," Sustainability, MDPI, vol. 10(6), pages 1-16, June.
    15. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    16. Yokote, Koji & Funaki, Yukihiko & Kamijo, Yoshio, 2017. "Coincidence of the Shapley value with other solutions satisfying covariance," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 1-9.
    17. R. Brânzei & E. Iñarra & S. Tijs & J. M. Zarzuelo, 2005. "Cooperation by Asymmetric Agents in a Joint Project," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 7(4), pages 623-640, October.
    18. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    19. Serrano, Roberto & Volij, Oscar, 1998. "Axiomatizations of neoclassical concepts for economies," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 87-108, August.
    20. Daniel Granot & Jeroen Kuipers & Sunil Chopra, 2002. "Cost Allocation for a Tree Network with Heterogeneous Customers," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 647-661, November.

    More about this item

    Statistics

    Access and download statistics

    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:82:y:2016:i:c:p:105-115. 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.