具有渐进策略的均势博弈的相关均衡点

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED

Mathematics of Operations Research Pub Date : 2024-04-29 DOI:10.1287/moor.2022.0357

Ofelia Bonesini, Luciano Campi, Markus Fischer

{"title":"具有渐进策略的均势博弈的相关均衡点","authors":"Ofelia Bonesini, Luciano Campi, Markus Fischer","doi":"10.1287/moor.2022.0357","DOIUrl":null,"url":null,"abstract":"In a discrete space and time framework, we study the mean field game limit for a class of symmetric N-player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows us to construct approximate N-player correlated equilibria that are robust with respect to progressive deviations. We illustrate our definition by way of an example with explicit solutions.Funding: O. Bonesini acknowledges financial support from Engineering and Physical Sciences Research Council [Grant EP/T032146/1]. M. Fischer acknowledges partial support through the University of Padua [Research Project BIRD229791 “Stochastic mean field control and the Schrödinger problem”].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"54 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Correlated Equilibria for Mean Field Games with Progressive Strategies\",\"authors\":\"Ofelia Bonesini, Luciano Campi, Markus Fischer\",\"doi\":\"10.1287/moor.2022.0357\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In a discrete space and time framework, we study the mean field game limit for a class of symmetric N-player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows us to construct approximate N-player correlated equilibria that are robust with respect to progressive deviations. We illustrate our definition by way of an example with explicit solutions.Funding: O. Bonesini acknowledges financial support from Engineering and Physical Sciences Research Council [Grant EP/T032146/1]. M. Fischer acknowledges partial support through the University of Padua [Research Project BIRD229791 “Stochastic mean field control and the Schrödinger problem”].\",\"PeriodicalId\":49852,\"journal\":{\"name\":\"Mathematics of Operations Research\",\"volume\":\"54 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of Operations Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1287/moor.2022.0357\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of Operations Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1287/moor.2022.0357","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

在离散时空框架下，我们基于相关均衡的概念研究了一类对称 N 人博弈的均场博弈极限。我们给出了相关解的定义，它允许我们构建近似的 N 人相关均衡，这种均衡在渐进偏差方面是稳健的。我们通过一个有明确解的例子来说明我们的定义：O. Bonesini 感谢工程与物理科学研究委员会的资助[Grant EP/T032146/1]。M. Fischer 感谢帕多瓦大学[研究项目 BIRD229791 "随机均值场控制和薛定谔问题"]的部分资助。

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

Correlated Equilibria for Mean Field Games with Progressive Strategies

In a discrete space and time framework, we study the mean field game limit for a class of symmetric N-player games based on the notion of correlated equilibrium. We give a definition of correlated solution that allows us to construct approximate N-player correlated equilibria that are robust with respect to progressive deviations. We illustrate our definition by way of an example with explicit solutions.Funding: O. Bonesini acknowledges financial support from Engineering and Physical Sciences Research Council [Grant EP/T032146/1]. M. Fischer acknowledges partial support through the University of Padua [Research Project BIRD229791 “Stochastic mean field control and the Schrödinger problem”].

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

Mathematics of Operations Research 管理科学-应用数学

CiteScore

3.40

自引率

5.90%

发文量

178

审稿时长

15.0 months

期刊介绍： Mathematics of Operations Research is an international journal of the Institute for Operations Research and the Management Sciences (INFORMS). The journal invites articles concerned with the mathematical and computational foundations in the areas of continuous, discrete, and stochastic optimization; mathematical programming; dynamic programming; stochastic processes; stochastic models; simulation methodology; control and adaptation; networks; game theory; and decision theory. Also sought are contributions to learning theory and machine learning that have special relevance to decision making, operations research, and management science. The emphasis is on originality, quality, and importance; correctness alone is not sufficient. Significant developments in operations research and management science not having substantial mathematical interest should be directed to other journals such as Management Science or Operations Research.