时变网络化博弈个体社会行为分析与控制

The analysis of individual social behavior in networked games is closely related to people's real life, which has important theoretical value and guiding significance to reality. However, because of the time-variant social network, the game process has become very complex, and there are many problems to be solved. Using the semi-tensor product method, the project studies the analysis and control problems for time-variant networked games (TNGs). First, the algebraic expression for the dynamics of TNGs is investigated, and a strict algebraic equation is constructed for the co-evolution of strategies and networks. Second, based on the algebraic expression of TNGs, the stable states, evolution trend and stable degree of strategy profiles are considered for TNGs, respectively, and several necessary and sufficient conditions are established. Third, in order to achieve the purpose of optimizing the game revenue, the corresponding algorithms are proposed to design the pinning control strategy, the event-triggered control strategy and so on. . The project is a challenging issue of networked games. The study of this issue can enrich the methodology of networked games，and can actively promote its applications in the fields of information transmission in wireless networks, the regulation and control of smart grid and so on.

网络化博弈中个体社会行为分析与人们实际生活密切相关，具有重要的理论价值和对现实的指导意义。但由于社会网络的时变性，博弈过程变得十分复杂，有很多问题亟待解决。本项目拟利用矩阵半张量积方法，从代数状态空间表示出发，研究时变网络化博弈的分析与控制问题。首先，研究时变网络化博弈的代数表示问题，建立策略和网络协同演化动态的严格代数方程。其次，基于博弈动态的代数表示，研究时变网络化博弈的稳定态、演化趋势、策略组合稳定度等问题，给出相应的充分或充要条件。最后，研究如何设计人为牵制控制策略、事件触发控制策略等来优化博弈的收益，建立相应的算法。. 本项目的研究是网络化博弈研究中一个富有挑战的问题，可丰富网络化博弈的研究方法和基础理论，进而积极推动其在无线网络信息传播、智能电网调控等领域的应用。

网络演化博弈动力学的研究，是探究群体社会行为演化的课题，近年来已经成为国际前沿研究问题。群体行为演化中的时变因素会严重破坏博弈演化的稳定性，使得长期最优决策难以实现，甚至使博弈演化变得不可控，值得深入研究。本项目为策略有限型时变网络演化博弈个体社会行为分析与控制建立了一种代数状态空间方法。经过项目组的合作研究，正式发表论文9篇，在审论文2篇，受此支撑获山东省高等学校科学技术奖一等奖1项。研究了时变网络演化博弈的代数表示问题，利用半张量积方法建立博弈演化动态的代数结构，即严格的数学方程。基于博弈动态的代数表示，研究了网络化博弈的纳什平衡点的存在性、稳定态、演化趋势、策略分组一致性等问题，给出若干充分、必要条件。考虑受扰动和不受扰动影响的情况，给出了可镇定状态反馈控制策略，鲁棒控制策略的设计方法，建立了若干算法来优化博弈的收益。我们的研究可丰富和发展网络演化博弈的研究方法和基础理论，从而为解决更多的实际问题提供了必要的理论和技术支撑。