本项目聚焦随机广义博弈中多元耦合和高度随机对纳什均衡分析和求解带来的挑战，围绕随机问题的博弈机制设计、随机广义纳什均衡解特性分析、博弈中随机参数和耦合约束的处理以及不同随机环境下均衡解算法设计等关键问题展开研究。首先，为克服耦合和随机带来的挑战，将控制理论反馈理念引入到多参与者博弈中，分析随机广义纳什均衡解的特性，证明特性成立的充分条件。其次，设计基于无模型学习的算法求解纳什均衡，突破基于梯度内核设计迭代算法的范式，避免基于随机参数模型做决策造成的效益损失，形成耦合随机问题建模成博弈模型进而获得最优决策的理论方法与技术路线。最后，将此理论研究成果扩展到能源互联网中，设计综合能源决策服务平台，面向用户和电管部门实时调度和决策开展应用验证，实现能源综合梯级利用和用户自律协同的智能调度。本项目的研究可丰富博弈的理论成果，并为能源互联网最优控制和决策体系的建设提供技术支撑。

Theoretical analyses and scalable seeking algorithms of Nash equilibria (NE) for stochastic generalized games featuring heterogeneous coupling and strong stochasticity are chief in game theory and application in order to achieve safe and efficient equilibria without excessive centralization of control decisions. The project studies the theory development of stochastic generalized games and their applications in ubiquitous electric Internet of things, counting the aspects of game mechanism design for stochastic problems, sufficient conditions for key characteristics of stochastic generalized NE, control methods for uncertainties and coupling constraints and NE seeking algorithms under different stochastic environments. The way to deal with uncertainties and coupling constraints relies on introducing the concept of feedback into multi-player games. This could avoid the efficiency loss caused by the decision-making process which depends on the modelling of uncertainties. Moreover, the NE seeking algorithms is designed by learning the uncertainty effects, which is actually data-enabled control, and breaks free from the paradigm of gradient based iterative procedures. Under the supervision of the developed theoretical results, a comprehensive energy decision-making service platform is designed to carry out the optimal energy management and real-time scheduling and decision-making for users and power management departments, which will promote the penetration of renewable energy and the participation ratio of users. This research will promote the theoretical development of stochastic generalized games. On one hand, it contributes to the reference of mechanism design for stochastic problems. On the other hand, it supports the optimal decision making under the coupled and stochastic environments. Moreover, the benefit on economics and society will be foreseen and realized by extending theoretical results to the electrical engineering.