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, Volume 23, Issue 3, pp 773–798 | Cite as

Monotonicity of the core-center of the airport game

  • Julio González-Díaz
  • Miguel Ángel Mirás Calvo
  • Carmen Quinteiro Sandomingo
  • Estela Sánchez Rodríguez
Original Paper

Abstract

One of the main goals of this paper is to improve the understanding of the way in which the core of a specific cooperative game, the airport game (Littlechild and Owen, Manag Sci 20:370–372, 1973), responds to monotonicity properties. Since such properties are defined for single-valued allocation rules, we use the core-center (González-Díaz and Sánchez-Rodríguez, Int J Game Theory 36:27–46, 2007) as a proxy for the core. This is natural, since the core-center is the center of gravity of the core and its behavior with respect to a given property can be interpreted as the “average behavior” of the core. We also introduce the lower-cost increasing monotonicity and higher-cost decreasing monotonicity properties that reflect whether a variation in a particular agent’s cost is beneficial to the other agents.

Keywords

Cooperative TU games Monotonicity Core Core-center  Airport games 

Mathematics Subject Classification

91A12 

Notes

Acknowledgments

We want to thank William Thomson for his encouragement and insight during the writing process of this manuscript. Authors acknowledge the financial assistance of the Spanish Ministry for Science and Innovation through projects MTM2011-27731-C03, ECO2009-14457-C0401ECON, and from the Xunta de Galicia through project INCITE09-207-064-PR.

References

  1. Arin J (2013) Monotonic core solutions: beyond Young’s theorem. Int J Game Theory 42:325–337CrossRefGoogle Scholar
  2. Calleja P, Rafels C, Tijs S (2009) The aggregate-monotonic core. Games Econ Behav 66:742–748CrossRefGoogle Scholar
  3. Getán J, Montes J, Rafels C (2009) A note on the monotonic core. Int Game Theory Rev 11:229–235CrossRefGoogle Scholar
  4. Gillies DB (1953) Some theorems on \(n\)-person games. PhD thesis, PrincetonGoogle Scholar
  5. González-Díaz J, Mirás-Calvo, MA, Quinteiro-Sandomingo C, Sánchez-Rodríguez E(2014) On the core of an airport game and the properties of its center. Reports in statistics and operations research. University of Santiago de Compostela 14(01):1–32Google Scholar
  6. González-Díaz J, Sánchez-Rodríguez E (2007) A natural selection from the core of a TU game: the core-center. Int J Game Theory 36:27–46CrossRefGoogle Scholar
  7. Housman D, Clark L (1998) Core and monotonic allocation methods. Int J Game Theory 27:611–616CrossRefGoogle Scholar
  8. Littlechild SC, Owen G (1973) A simple expression for the Shapley value in a special case. Manag Sci 20:370–372CrossRefGoogle Scholar
  9. Megiddo N (1974) On the nonmonotonicity of the bargaining set, the kernel and the nucleolus of a game. Siam J Appl Math 27:355–358CrossRefGoogle Scholar
  10. Mirás-Calvo MA, Quinteiro-Sandomingo C, Sánchez-Rodríguez E (2014) Monotonicity implications to the ranking of rules for airport problems. MimeoGoogle Scholar
  11. Thomson W (2007) Cost allocation and airport problems. Rochester Center for Economic Research Working PaperGoogle Scholar
  12. Young H (1985) Monotonic solutions of cooperatives games. Int J Game Theory 14:65–72CrossRefGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2015

Authors and Affiliations

  • Julio González-Díaz
    • 1
  • Miguel Ángel Mirás Calvo
    • 2
  • Carmen Quinteiro Sandomingo
    • 2
  • Estela Sánchez Rodríguez
    • 3
  1. 1.Departamento de Estatística e Investigación OperativaUniversidade de Santiago de CompostelaSantiago de CompostelaSpain
  2. 2.Departamento de MatemáticasUniversidade de VigoVigoSpain
  3. 3.Departamento de Estatística e Investigación OperativaUniversidade de VigoVigoSpain

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