Core Stability of Minimum Coloring Games
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Core Stability of Minimum Coloring Games
In cooperative game theory, a characterization of games with stable cores is known as one of the most notorious open problems. We study this problem for a special case of the minimum coloring games, introduced by Deng, Ibaraki & Nagamochi, which arises from a cost allocation problem when the players are involved in conflict. In this paper, we show that the minimum coloring game on a perfect gra...
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Some situations concerning cost allocation are formulated as combinatorial optimization games. We consider a minimum coloring game and a minimum vertex cover game. For a minimum coloring game, Deng{Ibaraki{Nagamochi 1] showed that deciding the core nonemptiness of a given minimum coloring game is NP-complete, which implies that a good characterization of balanced minimum coloring games is unlik...
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Submodularity (or concavity) is considered as an important property in the field of cooperative game theory. In this article, we characterize submodular minimum coloring games and submodular minimum vertex cover games. These characterizations immediately show that it can be decided in polynomial time that the minimum coloring game or the minimum vertex cover game on a given graph is submodular ...
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