Network slicing is a promising technology in 5G networks. The key concept is to divide the physical network into multiple logical networks, that are tailored to fulfill diverse service requirements. In this paper, we propose a multi-tenant radio access network (RAN) slicing approach that enables adaptive and isolated logical networks. We first formulate the multi-tenant RAN slicing problem as a centralized convex optimization problem that accounts for service resource requirements and ensures multi-tenant and multi-service isolation. Further, to reduce signaling load and preserve operator privacy, we portray the RAN slicing problem as a distributed non-cooperative game and prove the existence and uniqueness of a Nash equilibrium. We evaluate the efficiency of our distributed approach and then compare it with the state-of-the-art. Simulation results show that our distributed approach significantly improves resource utilization and operator satisfaction, while reducing computational complexity.