Inverse Matrix Games with Unique Nash Equilibrium

In an inverse game problem, one needs to infer the cost function of the players in a game such that a desired joint strategy is a Nash equilibrium. We study the inverse game problem for a class of multiplayer games, where the players' cost functions are characterized by a matrix. We guarantee that the desired joint strategy is the unique Nash equilibrium of the game with the inferred cost matrix. We develop efficient optimization algorithms for inferring the cost matrix based on semidefinite programs and bilevel optimization. We demonstrate the application of these methods using examples where we infer the cost matrices that encourages noncooperative players to achieve collision avoidance in path-planning and fairness in resource allocation.