Collaborative Research: Nash Equilibrium Problems under Uncertainty

合作研究：不确定性下的纳什均衡问题

• 批准号: 1538605
• 负责人: Jong-Shi Pang
• 金额: $ 31万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-15 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1538605&HistoricalAwards=false
• 关键词: Collaborative; Research; Nash; Equilibrium; Problems

Nash Equilibrium (NE) models provide the mathematical basis to study the interdependence between decision-makers in a competitive environment. These models provide insights into the operations of many multi-agent socio-technical systems, which include communications, electric power, and transportation networks. These socio-technical systems must not only accommodate technical constraints (e.g., physical laws of electrical power flow), but must also acknowledge the goals of several decision-makers, all of whom make choices under uncertainty and compete with their rivals. As a concrete example, consider the modern electricity network: some generation is carried out by large units, whereas distributed generation and storage may be operated by individuals, and transmission and distribution assets are operated by system operators and utilities. In addition, the growing penetration of renewable energy (highly volatile), the uncertainty about fuel prices, new technology, and energy policy, create a challenging setting in which the firms and/or individuals operate. This project, which combines the need to incorporate system constraints, as well as the effects of risk and uncertainty in the absence of cooperation across decision-makers, will address some of the most challenging questions regarding the structure, algorithms, scalability, and interpretations for NE models under uncertainty. The broader impact of the project includes the study of markets in power and communication networks, and the training and education of graduate students.Current theories and algorithmic schemes are relatively restrictive in their ability to accommodate risk measures, hierarchical and recourse-based decision-making, and coupled strategy sets. Motivated by these lacunae, this research will utilize a broad framework that can accommodate both private and coupled constraints, allows for linear, quadratic and convex models for taking recourse, and captures risk-aversion through the incorporation of composite and deviation-based risk measures. The goals of this research include the following: (i) Analysis: Verifiable statements for the existence and uniqueness of the resulting equilibria through the analysis of the resulting risk-based variational and quasi-variational inequality problems; (ii) Algorithms: Design, analysis (convergence, complexity) and statistical properties of estimators derived on algorithms reliant on joint sampling and approximation schemes; and (iii) Applications: Problems in electricity markets and other areas of planning under competition and uncertainty will be considered in two-stage and hierarchical settings.

纳什均衡（NE）模型为研究竞争环境中决策者之间的相互依赖关系提供了数学基础。这些模型提供了对许多多智能体社会技术系统运行的深入了解，其中包括通信、电力和交通网络。这些社会技术系统不仅必须适应技术限制（例如电力流的物理定律），而且还必须承认多个决策者的目标，所有决策者都在不确定性下做出选择并与竞争对手竞争。举一个具体的例子，考虑现代电力网络：一些发电是由大型机组进行的，而分布式发电和存储可能由个人运营，输配电资产由系统运营商和公用事业公司运营。此外，可再生能源的日益普及（高度波动）、燃料价格、新技术和能源政策的不确定性，给公司和/或个人的经营环境带来了挑战。该项目结合了纳入系统约束的需要，以及在决策者之间缺乏合作的情况下风险和不确定性的影响，将解决有关结构、算法、可扩展性和解释的一些最具挑战性的问题。不确定性下的NE模型。该项目更广泛的影响包括电力和通信网络市场的研究，以及研究生的培训和教育。当前的理论和算法方案在适应风险度量、分层和基于资源的决策方面的能力相对有限。 ，以及耦合策略集。受这些缺陷的启发，本研究将利用一个广泛的框架，该框架可以容纳私人约束和耦合约束，允许使用线性、二次和凸模型进行追索，并通过结合复合和基于偏差的风险度量来捕获风险规避。本研究的目标包括以下内容： (i) 分析：通过分析由此产生的基于风险的变分和准变分不平等问题，对所得均衡的存在性和唯一性进行可验证的陈述； (ii) 算法：基于联合采样和近似方案的算法得出的估计器的设计、分析（收敛性、复杂性）和统计特性； (iii) 应用：竞争和不确定性下电力市场和其他规划领域的问题将在两阶段和分层环境中考虑。