Monotonic Stable Solutions for Minimum Coloring Games

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For the class of minimum coloring games (introduced by Deng et al. (1999)) we investigate the existence of population monotonic allocation schemes (introduced by Sprumont (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
Place of PublicationTilburg
Publication statusPublished - 2011

Publication series

NameCentER Discussion Paper


  • Minimum coloring game
  • population monotonic allocation scheme
  • (P4
  • 2K2)-free graph
  • quasi-threshold graph


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