ABSTRACT
A multi-player stochastic noncooperative tracking game (NTG) with a conflicting target strategy and a cooperative tracking game (CTG) with a common target strategy of a mean-field stochastic jump diffusion system with external disturbance are investigated in this chapter. Due to the mean (collective) behavior in the system dynamic and cost function, the design of the NTG and CTG strategies for target tracking of the MFSJD system is more difficult than that of the conventional stochastic system. By the proposed indirect method, the NTG and CTG strategy design problems are transformed into a linear matrix inequality–constrained multi-objective optimization problem and LMI-constrained single-objective optimization problem, respectively. The LMI-constrained MOP can be solved effectively for all Nash equilibrium solutions of NTG at the Pareto front by the proposed reverse-order LMI-constrained multi-objective evolutionary algorithm. Two simulation examples, market share allocation and network security strategies in a cyber-social system, are given to illustrate the design procedure and validate the effectiveness of the proposed LMI-constrained MOEA for all Nash equilibrium solutions of NTG strategies of the MFSJD system.
