Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, June 03, 2004, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Yoshio Okamoto

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 (1999), which arises from a cost allocation problem when the players are involved in conflict. In this work, we show that the minimum coloring game on a perfect graph has a stable core if and only if every vertex of the graph belongs to a maximum clique. With this characterization, we can determine whether a given perfect graph yields a game with stable core in polynomial time. We also consider the problem on the core largeness, the extendability, and the exactness of minimum coloring games, and show that for perfect graphs these three properties are equivalent and also equivalent to that every clique of the graph is contained in a maximum clique. As a consequence, we show that it is hard to check these properties.

(Joint work with Thomas Bietenhader)

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