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Monotonic stable solutions for minimum coloring games

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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 \((P_4,2K_2)\)-free (or, equivalently, if its complement graph \(\bar{G}\) is quasi-threshold). Moreover, we provide a procedure that for these graphs always selects an integer population monotonic allocation scheme.

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Correspondence to H. Norde.

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The authors are indebted to two anonymous referees for their useful comments to an earlier version of this paper.

S. Miquel: Financial support by AGAUR.

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Hamers, H., Miquel, S. & Norde, H. Monotonic stable solutions for minimum coloring games. Math. Program. 145, 509–529 (2014). https://doi.org/10.1007/s10107-013-0655-y

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