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Marginality and Myerson values

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  • Manuel, C.
  • Ortega, E.
  • del Pozo, M.

Abstract

The aim of this paper is to analyze the relationship between marginality and the Myerson value, the within groups Myerson value (WG-Myerson value) and the between groups Myerson value (BG-Myerson value). We enlarge the idea of the classical marginal contribution of a player to a coalition in a cooperative game. Besides this type of contribution, in games with cooperation restricted by a graph, a player can contribute to a coalition in other ways. For example, lending his links to the coalition but without joining it. We will call it the marginal contribution of the player’s links (L-marginal contribution). Also he can contribute to a coalition by joining it with his communication possibilities. This is the marginal contribution of the player with his links (PL-marginal contribution). According to this, we define the strong monotonicity of the allocation rules with respect to the L-marginal contributions (and the L-marginality); and similarly, the strong monotonicity with respect to the PL-marginal contributions (and the PL-marginality). We prove that the Myerson value, the WG-Myerson value and the BG-Myerson value can be characterized using as requirement PL-marginality, marginality and L-marginality, respectively (as well as other properties).

Suggested Citation

  • Manuel, C. & Ortega, E. & del Pozo, M., 2020. "Marginality and Myerson values," European Journal of Operational Research, Elsevier, vol. 284(1), pages 301-312.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:1:p:301-312
    DOI: 10.1016/j.ejor.2019.12.021
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    References listed on IDEAS

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    Cited by:

    1. Niharika Kakoty & Surajit Borkotokey & Rajnish Kumar & Abhijit Bora, 2024. "Weighted Myerson value for Network games," Papers 2402.11464, arXiv.org.
    2. Surajit Borkotokey & Sujata Goala & Niharika Kakoty & Parishmita Boruah, 2022. "The component-wise egalitarian Myerson value for Network Games," Papers 2201.02793, arXiv.org.
    3. Erfang Shan, 2023. "Marginality and a Characterization of the Owen Graph value," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 451-461, June.
    4. Sylvain Béal & Florian Navarro, 2020. "Necessary versus equal players in axiomatic studies," Post-Print hal-03252179, HAL.
    5. C. Manuel & E. Ortega & M. del Pozo, 2023. "Marginality and the position value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 459-474, July.

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