Indefinite Mean-Field Stochastic Cooperative Linear-Quadratic Dynamic Difference Game With Its Application to the Network Security Model
研究了有限时域不定均值场随机合作线性二次差分博弈，通过加权耦合广义差分Riccati方程和Lyapunov方程，给出了获取所有帕累托最优决策向量的充要条件与算法，并用网络安全博弈验证了结果。
In this article, we show how to obtain all of the Pareto optimal decision vectors and solutions for the finite horizon indefinite mean-field stochastic cooperative linear-quadratic (LQ) difference game. First, the equivalence between the solvability of the introduced N coupled generalized difference Riccati equations (GDREs) and the solvability of the multiobjective optimization problem is established. However, it is difficult to obtain Pareto optimal decision vectors based on the N coupled GDREs because the optimal joint strategy adopted by all players to optimize the performance criterion of some players in the game is different from the strategies of other players, which rely on the weighted matrices of cost functionals that may be different among players. Second, a necessary and sufficient condition is developed to guarantee the convexity of the costs, which makes the weighting technique not only sufficient but also necessary for searching Pareto optimal decision vectors. It is then shown that the mean-field Pareto optimality algorithm (MF-POA) is presented to identify, in principle, all of the Pareto optimal decision vectors and solutions via the solutions to the weighted coupled GDREs and the weighted coupled generalized difference Lyapunov equations (GDLEs), respectively. Finally, a cooperative network security game is reported to illustrate the results presented. Simulation results validate the solvability, correctness, and efficiency of the proposed algorithm.