线性二次正反向平均场系统的混合纳什博弈与社会最优

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Xinwei Feng, Yiwei Lin
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引用次数: 0

摘要

我们考虑了一类新的混合线性二次纳什博弈和两种交互智能体的社会优化。一个被称为大代理,其他的被称为小代理。通过“混合”,我们的意思是所有的小代理相互组队来与这个大代理竞争,因为他们的成本函数是矛盾的。与标准设置不同的是,这个major的状态是由一些线性随机微分方程控制的,其中扩散项和漂移项都包含一个控制过程,而这些minor的状态都是弱耦合的,并且是由一些线性倒向随机微分方程驱动的,因为它们的终端条件是指定的。为了分别构建这两类智能体的分散策略,采用了变分方法和平均场近似相结合的反向逐人优化方法。在适当的条件下,我们还验证了这些分散策略的渐近最优性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mixed Nash games and social optima for linear-quadratic forward-backward mean-field systems
We consider a new class of mixed linear-quadratic Nash games and social optimization for two types of interactive agents. One is called a major agent and the others are minor agents. By 'mixed', we mean that all minor agents team up with each other to compete against this major agent for their contradictory cost functions. Different from the standard setup, this major's state is governed by some linear stochastic differential equation where the diffusion term and drift term both contain a control process, while the states of these minors are all weakly-coupled and driven by some linear backward stochastic differential equations because their terminal conditions are specified. To construct decentralized strategies for these two types of agents respectively, the backward person-by-person optimization method, combining some variational method and mean-field approximation are applied. Under some suitable conditions, we also verify the asymptotic optimality of these decentralized strategies.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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