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: 1538193
• 负责人: Uday Shanbhag
• 金额: $ 11万
• 依托单位: Pennsylvania State Univ University Park
• 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=1538193&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.

NASH平衡（NE）模型提供了数学基础，以研究竞争环境中决策者之间的相互依存关系。 这些模型为许多多机构社会技术系统的运营提供了见解，包括通信，电力和运输网络。 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），而且还必须承认几个决策者的目标，他们所有人都在不确定性下做出选择并与竞争对手竞争。 作为具体的例子，请考虑现代电力网络：某些一代是由大型单位进行的，而分布式生成和存储可以由个人操作，并且传输和分配资产由系统运营商和公用事业运营。 此外，可再生能源（高度波动）的渗透率不断增长，燃油价格，新技术和能源政策的不确定性创造了一个具有挑战性的环境，在该环境中，公司和/或个人在其中运作。该项目结合了整合系统限制的需求，以及在跨决策者之间没有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，可伸缩性和解释的一些最具挑战性的问题不确定性下的NE模型。该项目的更广泛影响包括对电力和通信网络市场的研究，以及研究生的培训和教育。流通的理论和算法方案在适应风险措施，基于等级和求助决策的能力方面相对限制和耦合策略集。这项研究将在这些空白的启发下，利用一个可以容纳私人和耦合约束的广泛框架，允许线性，二次和凸模型进行追索，并通过融合基于复合的风险和基于偏差的风险度量来捕捉风险避免风险。这项研究的目标包括以下内容：（i）分析：通过分析基于风险的变异和准变量不平等问题的分析，对所产生均衡的存在和唯一性的可验证陈述； （ii）算法：依赖于关节采样和近似方案的算法上的估计器的设计，分析（收敛，复杂性）和统计特性； （iii）申请：在竞争和不确定性下的电力市场和其他计划领域的问题将在两阶段和分层设置中考虑。