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, Volume 23, Issue 3, pp 773–798

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 

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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