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

A. Skoda ()
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A. Skoda: Université de Paris I

Mathematical Methods of Operations Research, 2021, vol. 93, issue 1, No 1, 32 pages

Abstract: 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.

Keywords: Cooperative game; Convexity; Graph-restricted game; Graph partitions; 91A12; 91A43; 90C27; 05C75 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00186-020-00728-4

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