A MODEL OF GRAPH COLORING DYNAMICS WITH ATTENTION WAVES AND STRATEGIC WAITING

Recently, Kearns et al. [Kearns, M., Suri, S. and Montfort, N., An experimental study of the coloring problem on human subject networks, Science 313 (2006) 824–827] studied the topology dependence of graph coloring dynamics. In their empirical study, the authors analyze, how a network of human subjects acting as autonomous agents performs in solving a conflict-avoidance task (the graph coloring problem) for different network architectures. A surprising result was that the run-time of the empirical dynamics decreases with the number of shortcuts in a Watts–Strogatz small-world graph. In a simulation of the dynamics based on randomly selecting color conflicts for update, they observe a strong increase of the run-time with the number of shortcuts. Here, we propose classes of strategies, which are capable of explaining the decrease in run-time with an increasing number of shortcuts. We show that the agent's strategy, the graph topology, and the complexity of the problem (essentially given by the graph's chromatic number) interact nontrivially yielding unexpected insights into the problem-solving capacity of organizational structures.