Abstract
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 language | English |
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Pages (from-to) | 509-529 |
Journal | Mathematical Programming |
Volume | 145 |
Issue number | 1-2 |
Early online date | 16 Mar 2014 |
DOIs | |
Publication status | Published - 1 Jun 2014 |