  $ $This paper addresses the inverse problem for Linear-Quadratic (LQ)
nonzero-sum $N$-player differential games, where the goal is to learn
parameters of an unknown cost function for the game, called observed, given the
demonstrated trajectories that are known to be generated by stationary linear
feedback Nash equilibrium laws. Towards this end, using the demonstrated data,
a synthesized game needs to be constructed, which is required to be equivalent
to the observed game in the sense that the trajectories generated by the
equilibrium feedback laws of the $N$ players in the synthesized game are the
same as those demonstrated trajectories. We show a model-based algorithm that
can accomplish this task using the given trajectories. We then extend this
model-based algorithm to a model-free setting to solve the same problem in the
case when the system's matrices are unknown. The algorithms combine both
inverse optimal control and reinforcement learning methods making extensive use
of gradient descent optimization for the latter. The analysis of the algorithm
focuses on the proof of its convergence and stability. To further illustrate
possible solution characterization, we show how to generate an infinite number
of equivalent games, not requiring to run repeatedly the complete algorithm.
Simulation results validate the effectiveness of the proposed algorithms.
