This paper presents a potential game-based method for the non-myopic planning of mobile sensor networks in the context of target tracking. The planning objective is to select the sequence of sensing points over more than one future time step to maximize information about the target states. This multistep lookahead scheme aims to overcome getting trapped at local information maximum when there are gaps in the sensing coverage due to constraints of the sensor platform mobility or limitations in sensing capabilities. However, long-term planning becomes computationally intractable as the length of planning horizon increases. This paper develops a game-theoretic approach to address the computational challenges. The main contributions of this paper are twofold: 1) to formulate a non-myopic planning problem for tracking multiple targets in a potential game, the size of which increases linearly as the number of planning steps and 2) to design a learning algorithm exploiting the joint strategy fictitious play and dynamic programming, which overcomes the gaps in sensing coverage. The numerical examples of multi-target tracking demonstrate that the proposed method gives a better estimation performance than myopic planning and is computationally tractable.