Inverse two-player zero-sum dynamic games

In this paper, we consider the problem of inverse dynamic games: given the observed behaviour of players during a dynamic game in equilibrium, how can we determine the underlying objective functions of the game? Whereas previous work in the literature has focused on inverse static games, our work focuses on inverse dynamic games. In particular, we address the problem of estimating the unknown parameters of the objective function of a two-player zero-sum dynamic game in open-loop Nash equilibrium. We exploit necessary conditions for equilibrium in a two-player zero-sum dynamic game to develop sufficient conditions for solving the two-player zero-sum inverse dynamic game problem. The sufficient conditions hold under assumptions on the control constraints and convexity of the game dynamics, and transform the inverse two-player zero-sum dynamic game problem into the problem of solving a system of linear equations. We apply our results to a linear quadratic two-player zero-sum game, and illustrate the recovery of objective function parameters from state and control equilibrium trajectories.