On ε-Nash equilibria of linear time-delay dynamic games with convex strategy set. Issue 13 (September 2022) - Zhao, Jingyi
Abstract: In this paper, the discrete-time, finite horizon, linear dynamic games with time-delay are considered. Firstly, the linear dynamic games with input-delay or state-delay where per-stage payoff functions are linear are proved to be potential games with the help of the semi-tensor product of matrices, respectively. Then, using an inscribed polyhedron to approximate the convex strategy set of the game, the problem of searching ε -Nash equilibrium of the linear time-delay dynamic game is transformed into a Nash equilibrium searching problem for a game with a finite strategy set. Furthermore, a searching algorithm for Nash equilibrium of the game with a finite strategy set is proposed. Finally, the effectiveness of the algorithm is verified by two examples.