This paper studies opportunistic spectrum sharing strategy (i.e., quantized precoding strategy) selection for cognitive multiple-input multiple-output multiple access channels with limited feedback under interference power constraint and maximum transmission stream number constraint. We put forward a game-theoretic framework to model the precoding strategy selection behaviors of the secondary users under the specified constraints. First, we prove the formulated discrete game is a potential game which possesses at least one feasible pure strategy Nash equilibrium. The feasibility and optimality of the Nash equilibrium are also analyzed. Then we prove that the solution to the sum rate maximization problem constitutes a feasible pure strategy Nash equilibrium of our formulated game. Furthermore, we design two algorithms. The iterative precoding strategy selection algorithm based on the best response rule is designed to attain a feasible Nash equilibrium. The modified algorithm is designed to improve the sum rate performance. Simulation results show that our designed algorithms can achieve optimal or near optimal sum rate performance with low complexity.