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Allocation rules for communication situations with incompatibilities

Author

Listed:
  • Manuela Basallote

    (University of Seville)

  • José M. Gallardo

    (University of Seville)

  • Carmen Hernández-Mancera

    (University of Seville)

  • Andrés Jiménez-Losada

    (University of Seville)

Abstract

In this article we analyze certain situations with restricted cooperation. To do this we introduce a model that combines two types of games well studied in the literature: graph-restricted games and games with incompatible players. In particular, our model extends Myerson’s model for communication situations and Bergantiños’ model for incompatible relationships. Our approach is based on the concept of profit measure, which allows us to deal simultaneously with both types of bilateral relationships. We show that in the situations considered there are multiple possible definitions of the profit achievable for each coalition. This leads us to introduce different allocation rules for these cooperative situations.

Suggested Citation

  • Manuela Basallote & José M. Gallardo & Carmen Hernández-Mancera & Andrés Jiménez-Losada, 2024. "Allocation rules for communication situations with incompatibilities," Annals of Operations Research, Springer, vol. 340(2), pages 757-784, September.
    • Handle: RePEc:spr:annopr:v:340:y:2024:i:2:d:10.1007_s10479-024-06145-8
    DOI: 10.1007/s10479-024-06145-8
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    References listed on IDEAS

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    1. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    2. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, vol. 51(1), pages 128-154, April.
    3. Antonio C. Alarcón & José M. Gallardo & Andrés Jiménez-Losada, 2022. "A Value for Graph-Restricted Games with Middlemen on Edges," Mathematics, MDPI, vol. 10(11), pages 1-15, May.
    4. Calvo, Emilio & Lasaga, Javier & van den Nouweland, Anne, 1999. "Values of games with probabilistic graphs," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 79-95, January.
    5. Sylvain Béal & André Casajus & Frank Huettner, 2015. "Efficient extensions of the Myerson value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 819-827, December.
    6. Manuel, C. & Ortega, E. & del Pozo, M., 2020. "Marginality and Myerson values," European Journal of Operational Research, Elsevier, vol. 284(1), pages 301-312.
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