Chromatic scheduling and frequency assignment
Discrete Applied Mathematics - Special volume: viewpoints on optimization
Journal of the ACM (JACM)
Maximizing the Number of Connections in Optical Tree Networks
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Graphs and Hypergraphs
A Game Theoretic Approach for Efficient Graph Coloring
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Distributed game-theoretic vertex coloring
OPODIS'10 Proceedings of the 14th international conference on Principles of distributed systems
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We study a strategic game where every node of a graph is owned by a player who has to choose a color. A player's payoff is 0 if at least one neighbor selected the same color, otherwise it is the number of players who selected the same color. The social cost of a state is defined as the number of distinct colors that the players use. It is ideally equal to the chromatic number of the graph but it can substantially deviate because every player cares about his own payoff, whatever how bad the social cost is. Following a previous work done by Panagopoulou and Spirakis [1] on the Nash equilibria of the coloring game, we give worst case bounds on the social cost of stable states. Our main contribution is an improved (tight) bound for the worst case social cost of a Nash equilibrium, and the study of strong equilibria, their existence and how far they are from social optima.