有知情大玩家的堆叠尔伯格问题中的均场博弈

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-06-13 DOI:10.1137/23m1615188

Philippe Bergault, Pierre Cardaliaguet, Catherine Rainer

{"title":"有知情大玩家的堆叠尔伯格问题中的均场博弈","authors":"Philippe Bergault, Pierre Cardaliaguet, Catherine Rainer","doi":"10.1137/23m1615188","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1737-1765, June 2024. <br/> Abstract. We investigate a stochastic differential game in which a major player has private information (the knowledge of a random variable), which she discloses through her control to a population of small players playing in a Nash mean field game equilibrium. The major player’s cost depends on the distribution of the population, while the cost of the population depends on the random variable known by the major player. We show that the game has a relaxed solution and that the optimal control of the major player is approximatively optimal in games with a large but finite number of small players.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mean Field Games in a Stackelberg Problem with an Informed Major Player\",\"authors\":\"Philippe Bergault, Pierre Cardaliaguet, Catherine Rainer\",\"doi\":\"10.1137/23m1615188\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1737-1765, June 2024. <br/> Abstract. We investigate a stochastic differential game in which a major player has private information (the knowledge of a random variable), which she discloses through her control to a population of small players playing in a Nash mean field game equilibrium. The major player’s cost depends on the distribution of the population, while the cost of the population depends on the random variable known by the major player. We show that the game has a relaxed solution and that the optimal control of the major player is approximatively optimal in games with a large but finite number of small players.\",\"PeriodicalId\":49531,\"journal\":{\"name\":\"SIAM Journal on Control and Optimization\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-06-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Control and Optimization\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1615188\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Control and Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1615188","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}

引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 3 期第 1737-1765 页，2024 年 6 月。摘要。我们研究了一个随机微分博弈，在这个博弈中，主要博弈者拥有私人信息（随机变量的知识），她通过控制权将这些信息透露给在纳什均场博弈均衡中博弈的小博弈者群体。主要玩家的成本取决于群体的分布，而群体的成本则取决于主要玩家已知的随机变量。我们证明了博弈有一个松弛解，而且在小博弈者数量众多但有限的博弈中，主要博弈者的最优控制近似最优。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Mean Field Games in a Stackelberg Problem with an Informed Major Player

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1737-1765, June 2024.
Abstract. We investigate a stochastic differential game in which a major player has private information (the knowledge of a random variable), which she discloses through her control to a population of small players playing in a Nash mean field game equilibrium. The major player’s cost depends on the distribution of the population, while the cost of the population depends on the random variable known by the major player. We show that the game has a relaxed solution and that the optimal control of the major player is approximatively optimal in games with a large but finite number of small players.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.