We consider the uplink transmission between a multi-antenna ground station and an unmanned aerial vehicle (UAV) swarm. The UAVs are assumed as intelligent agents, which can explore their optimal three dimensional (3-D) deployment to maximize the channel capacity of the multiple input multiple output (MIMO) system. Specifically, considering the limitations of each UAV in accessing the global information of the network, we focus on a decentralized control strategy by noting that each UAV in the swarm can only utilize the local information to achieve the optimal 3-D deployment. In this case, the optimization problem can be divided into several optimization sub-problems with respect to the rank function. Due to the non-convex nature of the rank function and the fact that the optimization sub-problems are coupled, the original problem is NP-hard and, thus, cannot be solved with standard convex optimization solvers. Interestingly, we can relax the constraint condition of each sub-problem and solve the optimization problem by a formulated UAVs channel capacity maximization game. We analyze such game according to the designed reward function and the potential function. Then, we discuss the existence of the pure Nash equilibrium in the game. To achieve the best Nash equilibrium of the MIMO system, we develop a decentralized learning algorithm, namely decentralized UAVs channel capacity learning. The details of the algorithm are provided, and then, the convergence, the effectiveness and the computational complexity are analyzed, respectively. Moreover, we give some insightful remarks based on the proofs and the theoretical analysis. Also, extensive simulations illustrate that the developed learning algorithm can achieve a high MIMO channel capacity by optimizing the 3-D UAV swarm deployment with the local information.