CAREER: Stochastic Games on Large Graphs in the Mean Field Regime and Beyond

职业：平均场制度及其他大图上的随机博弈

基本信息

批准号：
2045328
负责人：
Daniel Lacker
金额：
$ 42.66万
依托单位：
Columbia University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-07-01 至 2026-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2045328&HistoricalAwards=false
关键词：
CAREER Stochastic Games Large Graphs

项目摘要

Diverse areas of science rely on mathematical models of large-scale systems of interacting and competing agents. The agents may be investors, drivers, or viruses, and the large systems may be financial markets, highways, or epidemics, for example. The most widely used framework for modeling competition between many interacting agents, known as "mean field game theory," is fundamentally limited in scope to symmetric models, in which each agent interacts equally with each of the others. Many important phenomena, on the other hand, are governed by networks---such as those formed by social ties or financial obligations – that determine which agents interact with each other. Network structures have important implications that the standard theory cannot capture. This project tackles this limitation by developing new mathematical frameworks to handle large-scale models of competition with heterogeneous interactions governed by networks. Both graduate and undergraduate students are involved in the research activities, and local K-12 outreach efforts are designed to foster an interest in applied mathematics and continued education.This project builds a rigorous foundation for a new era of network-based mean field game theory and applications. The first goal is to identify the range of network structures for which the standard mean field approximation is valid, in order to substantially extend the scope of the mean field paradigm. For those network structures for which the standard mean field approximation fails, the second goal is to identify and analyze tractable alternatives. Certain important features of mean field approximations, such as asymptotic independence, fail in sparse (as opposed to dense) networks, and the third goal of the research is to identify precise sparsity thresholds for this and other phenomena. This project adapts and extends recent methodologies of graph limit theories and large deviations, which have a strong track record of solving network-based problems in statistical physics. New mathematical challenges arise in the game-theoretic setting due to the long-range dependencies induced by competitive equilibrium, and new techniques must be developed to address these challenges.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

科学的各个领域依赖于相互作用和竞争代理的大规模系统的数学模型。代理商可能是投资者，驱动因素或病毒，例如，大型系统可能是金融市场，高速公路或流行病。在许多相互作用的代理（称为“平均现场游戏理论”）之间建模竞争的最广泛使用的框架从根本上限制了对称模型的范围，在这种模型的范围上，每个代理都与其他每个代理都平等相互作用。另一方面，许多重要现象受网络的约束，例如由社会关系或财务义务形成的网络，这些现象决定了哪些代理人相互作用。网络结构具有标准理论无法捕获的重要含义。该项目通过开发新的数学框架来应对这一限制，以处理由网络控制的异质相互作用的大规模竞争模型。研究生和本科生都参与研究活动，本地K-12外展工作旨在促进对应用数学和持续教育的兴趣。该项目为基于网络的平均现场游戏理论和应用的新时代建立了严格的基础。第一个目标是确定标准平均场近似有效的网络结构范围，以实质上扩展平均场范式的范围。对于那些针对平均场近似的某些重要特征的网络结构失败，第二个目标是识别和分析可处理的替代方案。平均场近似值的某些重要特征，例如不对称独立性，在稀疏（而不是密度）网络中失败，研究的第三个目标是确定这种和其他现象的精确稀疏阈值。该项目适应并扩展了最新的图表限制理论和较大的出发方法，这些方法在解决基于网络的物理问题的问题方面具有很强的记录。由于竞争性同等的远程依赖性，必须在游戏理论环境中出现新的数学挑战，并且必须开发新的技术来应对这些挑战。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和更广泛影响的审查标准来通过评估而被认为是珍贵的支持。