A Hierarchical Game Approach to Inter-Operator Spectrum Sharing
Mehdi Bennis, Mérouane Debbah, Samson Lasaulce, Alagan Anpalagan · 2009
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.