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Inheritance of convexity for the $$\mathcal {P}_{\min }$$ P min -restricted game

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  • A. Skoda

    (Université de Paris I)

Abstract

We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the sub-components corresponding to a minimum partition. This minimum partition $$\mathcal {P}_{\min }$$ P min is induced by the deletion of the minimum weight edges. We provide a characterization of the graphs satisfying inheritance of convexity from the underlying game to the restricted game associated with $$\mathcal {P}_{\min }$$ P min . Moreover, we prove that these graphs can be recognized in polynomial time.

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  • A. Skoda, 2021. "Inheritance of convexity for the $$\mathcal {P}_{\min }$$ P min -restricted game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 1-32, February.
    • Handle: RePEc:spr:mathme:v:93:y:2021:i:1:d:10.1007_s00186-020-00728-4
    DOI: 10.1007/s00186-020-00728-4
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    References listed on IDEAS

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    6. Alexandre Skoda, 2019. "Convexity of graph-restricted games induced by minimum partitions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01617023, HAL.
    7. Alexandre Skoda, 2019. "Convexity of graph-restricted games induced by minimum partitions," Post-Print halshs-01617023, HAL.
    8. Marco Slikker, 2000. "Inheritance of properties in communication situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(2), pages 241-268.
    9. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2000. "The position value for union stable systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 221-236, November.
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