Coalition Pareto-Optimal Solution in a Nontransferable Game

IF 0.5 4区 数学 Q3 MATHEMATICS
V. I. Zhukovskiy, L. V. Zhukovskaya, L. V. Smirnova
{"title":"Coalition Pareto-Optimal Solution in a Nontransferable Game","authors":"V. I. Zhukovskiy,&nbsp;L. V. Zhukovskaya,&nbsp;L. V. Smirnova","doi":"10.1134/S1064562424702430","DOIUrl":null,"url":null,"abstract":"<p>By the end of the last century, four directions had been established in the mathematical theory of positional differential games (PDGs): a noncoalition version of PDG, a cooperative, hierarchical, and, finally, the least studied, a coalition version of PDG. In turn, within the coalition, there are usually games with transferable payoffs (with side payments, when players can share their winnings during the game) and nontransferable payoffs (games with side payments, when such redistributions are absent for one reason or another). Studies of coalition games with side payments are concentrated and actively conducted at the Faculty of Applied Mathematics and Management Processes of St. Petersburg University and Institute of Applied Mathematical Research of the Karelian Research Centre of Russian Academy of Sciences (L.A. Petrosyan, V.V. Mazalov, E.M. Parilina, A.N. Rettieva, and their numerous domestic and foreign students). However, side payments are not always present even in economic interactions; moreover, side payments may be generally prohibited by law. The studies we have undertaken in recent years on the balance of threats and counterthreats (sanctions and countersanctions) in noncoalition differential games allow, in our opinion, covering some aspects of the nontransferable version of coalition games. This article is devoted to the issues of internal and external stability of coalitions in the PDG class. It reveals the coefficient constraints in the mathematical model of the positional differential linear-quadratic game of six persons with a two-coalition structure, in which this coalition structure is internally and externally stable.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2 supplement","pages":"S409 - S421"},"PeriodicalIF":0.5000,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424702430","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

By the end of the last century, four directions had been established in the mathematical theory of positional differential games (PDGs): a noncoalition version of PDG, a cooperative, hierarchical, and, finally, the least studied, a coalition version of PDG. In turn, within the coalition, there are usually games with transferable payoffs (with side payments, when players can share their winnings during the game) and nontransferable payoffs (games with side payments, when such redistributions are absent for one reason or another). Studies of coalition games with side payments are concentrated and actively conducted at the Faculty of Applied Mathematics and Management Processes of St. Petersburg University and Institute of Applied Mathematical Research of the Karelian Research Centre of Russian Academy of Sciences (L.A. Petrosyan, V.V. Mazalov, E.M. Parilina, A.N. Rettieva, and their numerous domestic and foreign students). However, side payments are not always present even in economic interactions; moreover, side payments may be generally prohibited by law. The studies we have undertaken in recent years on the balance of threats and counterthreats (sanctions and countersanctions) in noncoalition differential games allow, in our opinion, covering some aspects of the nontransferable version of coalition games. This article is devoted to the issues of internal and external stability of coalitions in the PDG class. It reveals the coefficient constraints in the mathematical model of the positional differential linear-quadratic game of six persons with a two-coalition structure, in which this coalition structure is internally and externally stable.

不可转移对策中的联盟帕累托最优解
到上个世纪末,在位置微分博弈(PDG)的数学理论中已经建立了四个方向:PDG的非联盟版本,合作的,分层的,以及最后,研究最少的,PDG的联盟版本。反过来,在联盟中,通常存在具有可转移收益的游戏(玩家可以在游戏中分享他们的收益)和不可转移收益(游戏邦注:有附加收益的游戏,当这种再分配因某种原因而缺失时)。在圣彼得堡大学应用数学和管理过程学院和俄罗斯科学院卡累利阿研究中心应用数学研究所(L.A. Petrosyan, V.V. Mazalov, E.M. Parilina, A.N. Rettieva,以及他们众多的国内外学生),集中并积极地进行了具有侧面支付的联盟博弈的研究。然而,即使在经济互动中,附带支付也并不总是存在;此外,法律一般可能禁止额外付款。近年来,我们对非联盟微分博弈中威胁与反威胁(制裁与反制裁)的平衡进行的研究,在我们看来,涵盖了联盟博弈不可转让版本的某些方面。本文致力于讨论PDG类联盟的内部和外部稳定性问题。揭示了六人双联盟结构的位置微分线性二次对策数学模型中的系数约束,其中该联盟结构是内外稳定的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Doklady Mathematics
Doklady Mathematics 数学-数学
CiteScore
1.00
自引率
16.70%
发文量
39
审稿时长
3-6 weeks
期刊介绍: Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信