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

Alexandre Skoda ()
Alexandre Skoda: UP1 - Université Paris 1 Panthéon-Sorbonne, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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 Pmin 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 Pmin. Moreover, we prove that these graphs can be recognized in polynomial time.

Keywords: Cooperative game; Convexity; Graph-restricted game; Graph partitions (search for similar items in EconPapers)
Date: 2020-09-16
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-02960813
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Published in Mathematical Methods of Operations Research, Springer Verlag, 2020, ⟨10.1007/s00186-020-00728-4⟩

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