{"title":"线性二次正反向平均场系统的混合纳什博弈与社会最优","authors":"Xinwei Feng, Yiwei Lin","doi":"10.3934/mcrf.2023038","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mixed Nash games and social optima for linear-quadratic forward-backward mean-field systems\",\"authors\":\"Xinwei Feng, Yiwei Lin\",\"doi\":\"10.3934/mcrf.2023038\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/mcrf.2023038\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/mcrf.2023038","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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.
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.