Closed-loop and open-loop equilibrium of a class time-inconsistent linear-quadratic differential games

In this study, we concern with a class linear quadratic (LQ, for short) N-person differential games with time inconsistency, where the time inconsistency arises from non-exponential discount function. The notions of closed-loop and open-loop equilibrium strategy are introduced. We establish the equivalent relationship between time-inconsistent differential game problems, forward-backward type differential equations, and Riccati type differential equations in the framework of closed-loop and open-loop equilibrium, respectively. We provide an example of time-inconsistent differential games from which we find a time-consistent equilibrium strategy.