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Monotonicity of the core-center of the airport game

Author

Listed:
  • Julio González-Díaz
  • Miguel Mirás Calvo
  • Carmen Sandomingo
  • Estela Rodríguez

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. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:topjnl:v:23:y:2015:i:3:p:773-798
    DOI: 10.1007/s11750-014-0358-4
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    References listed on IDEAS

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    1. J. Arin, 2013. "Monotonic core solutions: beyond Young’s theorem," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 325-337, May.
    2. Calleja, Pedro & Rafels, Carles & Tijs, Stef, 2009. "The aggregate-monotonic core," Games and Economic Behavior, Elsevier, vol. 66(2), pages 742-748, July.
    3. 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.
    4. William Thomson, 2007. "Cost allocation and airport problems," RCER Working Papers 537, University of Rochester - Center for Economic Research (RCER).
    5. David Housman & (*), Lori Clark, 1998. "Note Core and monotonic allocation methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 611-616.
    6. 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.
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    Cited by:

    1. 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.
    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. 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.

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