  In this paper, we study a problem where multiple operators (OPs) need to
share a common pool of spectrum with each other. Our objective is to maximize
the social welfare, defined as the overall weighted sum rate of the OPs. The
problem is decomposed into two parts: the first part is to allocate RBs to OPs,
which we do so by extending the framework of many-to-one matching game with
externalities. The second part is to allocate power of small cell base stations
(SBSs) belonging to each OP, which is accomplished using reinforcement
learning. Assuming that the SBSs associated with each OPs are spatially
distributed according to Poisson point process (PPP), we show that pairwise
stable matchings achieve local maximas of the social welfare function. We
propose two algorithms to search for the stable matchings. Simulation results
show that these algorithms are well behaved in terms of convergence and
efficiency of the solutions.
