Pareto Optimality of Stochastic Mean-Field Delay Systems

This research focuses on identifying the necessary and sufficient conditions for achieving Pareto optimality in delayed cooperative differential games that are governed by mean-field stochastic differential equations over a finite horizon. We express the game problem as a set of constrained delayed mean-field stochastic optimal control problems. Through the application of the maximum principle for optimal control in mean-field stochastic delay differential systems, we derive the necessary condition for a Pareto efficient strategy. Additionally, we provide the sufficient condition under the convexity assumptions on certain functions. Finally, a linear quadratic optimal control problem is considered as an application of the theoretical findings.