Inverse Noncooperative Dynamic Games

We consider the problem of computing parameters of player cost functions in discrete-time nonzero-sum noncooperative dynamic games from open-loop Nash equilibria. Although similar inverse problems have been investigated in the optimal control literature where there is a single player (or decision maker), there has been limited attention given to the inverse dynamic game problem with multiple (competing) players. By exploiting the minimum principle of optimal control, we propose a method of inverse dynamic games for when the information structure of the game is open-loop. Our method involves solving a system of linear equations and is able to recover the true unknown parameters (up to an unknown scaling factor) whenever a testable rank condition holds. We illustrate our method in an example two-player game.