近年来，带泊松跳跃随机微分博弈成为控制科学、决策科学等领域研究的重点和热点，受到越来越多学者关注。本项目旨在利用Pareto策略与Stackelberg策略的性质，运用随机最优控制的理论和方法，从四个方面展开研究：（1）有限时域的情形下，研究Pareto解存在的必要条件及充分条件，并讨论Pareto有效策略及Pareto解的求解方法；（2）分析有限时域情形和无限时域情形的差异，研究无限时域的情形下Pareto解的存在条件及求解方法；（3）线性二次的情形下，研究开环Stackelberg策略的存在条件，并讨论开环Stackelberg策略的求解方法；（4）研究线性二次情形下反馈Stackelberg策略的存在条件以及求解方法。通过本项目的实施，可以进一步丰富和完善多目标控制理论，并推进数学相关理论及控制工程、经济学和管理学等相关学科的发展。

In recent years, stochastic differential game with Poisson jumps has become focus and hotspot in the fields of control science and decision-making science and has attracted more and more scholars' attention. Utilizing the properties of Pareto strategy and Stackelberg strategy, employing the theory and methods of stochastic optimal control, this project aims to carry out a study from four aspects: (i) We study the necessary and sufficient conditions for the existence of Pareto solutions in finite horizon, and discuss the calculation method of Pareto effective strategies and Pareto solutions. (ii) We analyze the difference between the finite horizon case and the infinite horizon situation, and discuss the existence conditions and the calculation method of Pareto solutions in infinite horizon. (iii) For the LQ case, we study the existence conditions of open-loop Stackelberg strategy, and discuss the calculation method of open-loop Stackelberg strategy. (iv) We research the existence conditions and the calculation method of feedback Stackelberg strategy for the LQ situation. In conclusion, by the implementation of this project, the multi-objective control theory can be further enriched and improved, and the development of related mathematical theory, control engineering, economics and management can also be promoted.