A network coloring game

Abstract

We analyze a network coloring game which was first proposed by Michael Kearns and others in their experimental study of dynamics and behavior in social networks. In each round of the game, each player, as a node in a network G, uses a simple, greedy and selfish strategy by choosing randomly one of the available colors that is different from all colors played by its neighbors in the previous round. We show that the coloring game converges to its Nash equilibrium if the number of colors is at least two more than the maximum degree. Examples are given for which convergence does not happen with one fewer color. We also show that with probability at least 1∈-∈δ, the number of rounds required is O(log(n/δ)). © 2008 Springer Berlin Heidelberg.