This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays. Not only the state variable, but also control variables of players involve discrete and distributed delays. By virtue of the duality method and the generalized anticipated backward stochastic differential equations, the author establishes a necessary maximum principle and a sufficient verification theorem. To explain theoretical results, the author applies them to a dynamic advertising game problem.

中文翻译：

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离散和分布时滞的非零和随机微分对策的最大原理

本技术说明涉及具有离散和分布式延迟的非零和随机差分博弈的最大原理。不仅状态变量而且游戏者的控制变量都涉及离散和分散的延迟。利用对偶方法和广义的预期后向随机微分方程，建立了必要的最大原理和充分的验证定理。为了解释理论结果，作者将其应用于动态广告游戏问题。