Pairwise nash and refereeing for resource allocation in self-organizing networks

This paper considers the allocation of frequency and time resources in a heterogeneous network, in a self-organizing manner. The general problem is to assign a resource set, so as to minimize the number of pairs of adjacent base stations that obtain the same resource. This can be modeled by Minimum-Collisions Coloring (MCC) on an undirected graph, where the colors are the resources, the vertices are the wireless nodes and the edges represent interference relations between nodes. The MCC decision problem is NP-complete. This paper develops a game-theoretic model for the MCC problem. The players of this game are a set of colored agents, which in practice could be software robots. The game is proven to possess multiple pure-strategy Nash Equilibria (NEs). Then a swapping mechanism is developed to improve the NE performance and the resulting coloring is shown to be pairwise-Nash stable. Further refinement is proposed by making use of an external referee. All theoretical results are corroborated through simulations.