Maximum Principle for Nonzero-Sum Stochastic Differential Game With Delays

In this technical note, we discuss a nonzero-sum stochastic differential game with delays. Not only the state variable, but also control variables of players involve delays. This kind of games are motivated by some interesting problems arising from economics and finance. Using anticipated backward stochastic differential equations, we establish a necessary condition and a sufficient condition of maximum principle for the delayed game problem. To explain theoretical results, we apply them to an economic problem.