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Cooperation when some players are incompatible

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Abstract

A situation with incompatibilities is defined to be a TU-game together with a graph whose arcs link pairs of incompatible players. In this paper we introduce an efficient and fair allocation rule which selects a payoff for every possible situation with incompatibilities (when the set of players is fixed), and prove that it is uniquely determined. Besides, we demonstrate that it is stable, study its relationship with the so-calledIR-Shapley value and show that it generalizes an earlier theory for simple games. Finally, the communication situations with incompatibilities are studied.

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Authors and Affiliations

  1. Department of Applied Economics, University of Vigo, Spain

    Gustavo Bergantiños

  2. Department of Applied Mathematics, Polytechnic University of Catalunya, Spain

    Francesc Carreras

  3. Departamento de Estadística e I.O., Facultad de Matemáticas, Universidad de Santiago de Compostela, 15771, Santiago de Compostela, Spain

    Ignacio García-Jurado

Authors
  1. Gustavo Bergantiños
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  2. Francesc Carreras
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  3. Ignacio García-Jurado
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Additional information

We thank University of Santiago de Compostela and Xunta de Galicia for financial support through projects 60902.25064(5060) and XUGA20701B91.

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Bergantiños, G., Carreras, F. & García-Jurado, I. Cooperation when some players are incompatible. ZOR - Methods and Models of Operations Research 38, 187–201 (1993). https://doi.org/10.1007/BF01414214

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  • DOI: https://doi.org/10.1007/BF01414214

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