A Hierarchical Game Approach to Inter-Operator Spectrum Sharing

In this paper, we address the problem of spectrum sharing where wireless (competitive) operators coexist in the same frequency band. First, we model this problem as a strategic non-cooperative game where operators simultaneously share the spectrum according to the Nash equilibrium (N.E). Given a set of channel realizations, several Nash equilibria exist which render the outcome of the game unpredictable. Second, the inter-operator spectrum sharing problem is reformulated as a hierarchical power allocation game, where one of the operators (i.e., primary) poses as a leader and the other operator (i.e., secondary) as a follower. Using backward induction, the Stackelberg equilibrium (S.E) is reached where the best response of the secondary operator is taken into account upon maximizing the primary operator´s payoff. It turns out that the Stackelberg approach yields better payoffs for operators compared to the classical greedy water-filling approach. Furthermore, to reach Pareto-efflcient boundaries, the spectrum sharing problem is formulated as a repeated game, where players interact over a longer period of time and learning from each other´s strategies. Numerical results provide a comparison between the non-cooperative, hierarchical and centralized approach.