  One of the many problems faced by current cellular network technology is the
under utilization of the dedicated, licensed spectrum of network operators. An
emerging paradigm to solve this issue is to allow multiple operators to share
some parts of each others' spectrum. Previous works on spectrum sharing have
failed to integrate the theoretical insights provided by recent developments in
stochastic geometrical approaches to cellular network analysis with the
objectives of network resource allocation problems. In this paper, we study the
non-orthogonal spectrum assignment with the goal of maximizing the social
welfare of the network, defined as the expected weighted sum rate of the
operators. We adopt the many-to-one stable matching game framework to tackle
this problem. Moreover, using the stochastic geometrical approach, we show that
its solution can be both stable as well as socially optimal. This allows for
computation of the game theoretical solution using generic Markov Chain Monte
Carlo method. We also investigate the role of power allocation schemes using
Q-learning, and we numerically show that the effect of resource allocation
scheme is much more significant than the effect of power allocation for the
social welfare of the system.
