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.