Monotonic stable solutions for minimum coloring games

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8 Citations (Scopus)


For the class of minimum coloring games (introduced by Deng et al. Math Oper Res, 24:751–766, 1999) we investigate the existence of population monotonic allocation schemes (introduced by Sprumont Games Econ Behav 2:378–394, 1990). We show that a minimum coloring game on a graph G has a population monotonic allocation scheme if and only if G is (P4,2K2) -free (or, equivalently, if its complement graph G‾ is quasi-threshold). Moreover, we provide a procedure that for these graphs always selects an integer population monotonic allocation scheme.
Original languageEnglish
Pages (from-to)509-529
JournalMathematical Programming
Issue number1-2
Early online date16 Mar 2014
Publication statusPublished - 1 Jun 2014


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