Nash Equilibria for scalar LQ games: iterative and data-driven algorithms

Determining Nash equilibrium solutions of nonzero-sum dynamic games is generally challenging. In this paper, we propose four different iterative algorithms for finding Nash equilibrium strategies of discrete-time scalar linear quadratic games, with strategy updates based on the solution of either Lyapunov or Riccati equations. Local convergence criteria are discussed. Motivated by the fact that in many practical scenarios each player in the game may have access to different (incomplete) information, we introduce purely data-driven implementations of the algorithms. This allows the players to reach a Nash equilibrium solution of the game via scheduled experiments and without knowledge of each other's performance criteria or of the system dynamics. The efficacy of the presented algorithms is illustrated via a numerical example.