  In this paper, we address the inverse problem in the case of linear-quadratic
discrete-time dynamic non-cooperative games. Given feedback laws of players
that are known to be a Nash equilibrium pair for a discrete-time linear system,
we want find cost function parameters for which the observed feedback laws are
optimal and stabilizing. Using the given feedback laws, we introduce a
model-based algorithm that generates cost function parameters solving the
problem. We provide theoretical results that guarantee the convergence and
stability of the algorithm as well as the way to generate new games with
necessary properties without requiring to run the complete algorithm repeatedly
. Then the algorithm is extended to a model-free version that uses data samples
generated by unknown dynamics and has the same properties as the model-based
version. Simulation results validate the effectiveness of the proposed
algorithms.
