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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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    1. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    2. Marco Slikker, 2000. "Inheritance of properties in communication situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(2), pages 241-268.
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    4. Alexandre Skoda, 2017. "Inheritance of convexity for partition restricted games," Post-Print halshs-01487381, HAL.
    5. van den Nouweland, Anne & Borm, Peter, 1991. "On the Convexity of Communication Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 421-430.
    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. Faigle, U. & Grabisch, M. & Heyne, M., 2010. "Monge extensions of cooperation and communication structures," European Journal of Operational Research, Elsevier, vol. 206(1), pages 104-110, October.
    8. repec:hal:pseose:hal-00803233 is not listed on IDEAS
    9. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    10. Alexandre Skoda, 2019. "Convexity of graph-restricted games induced by minimum partitions," Post-Print halshs-01617023, HAL.
    11. Alexandre Skoda, 2017. "Inheritance of convexity for partition restricted games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01487381, HAL.
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