This paper presents a resource allocation framework for device-to-device (D2D) communications underlaying uplink MIMO cellular networks. At first, our aim is to address the sum-rate maximization problem of the cellular network with both D2D and cellular users. An algorithm based on pure random search is presented for obtaining the optimal resource allocation without using an exhaustive search. Then, we propose a noncooperative resource allocation game for the joint self-optimization of channel allocation, power control, and precoding of the D2D users in a more practical setting. The feasibility and existence of the pure strategy Nash equilibrium are then established. An iterative algorithm based on best response dynamic is then proposed to determine the feasible pure strategy Nash equilibrium under specific conditions. As the algorithm may not always converge, we devise a strategy refinement mechanism to tackle this issue based on the sum-rate criterion. Simulation results verify our theoretical analysis and findings.