Turnpike property of nonzero-sum linear-quadratic differential games

This paper investigates the turnpike properties of deterministic nonzero-sum linearquadratic (LQ) differential games. Under certain assumptions on the Hamiltonian matrix of the nonzero-sum LQ differential game, we establish the solvability of both the coupled non-symmetric differential Riccati equation (DRE) and the algebraic Riccati equation (ARE). Moreover, we identify the convergence relationship between the DRE and ARE, which is essential for understanding the turnpike properties. Over a finite but sufficiently long time horizon, the open-loop Nash equilibrium is shown to remain exponentially close to the solution of a two-objective optimization problem for the majority of the time horizon.