Inter-operator spectrum sharing has been proposed to exploit spectrum efficiency in future communication system. By using game theory and learning algorithm, we design a partially distributed implementation method. Such a method is proven to reach the system equilibrium which improves spectrum efficiency between operators. Furthermore, by queueing analysis and robust potential game, we show that the convergence rate can be accelerated by incorporating more asynchronous operator systems. This distributed implementation method creates a low complexity solution for operators to realize inter-operator spectrum sharing for 3GPP LTE-A systems or similar.