非平衡合作博弈大联盟稳定解  

Stable solutions of grand coalitions in unbalanced cooperative games

作　　者：刘林冬 吴子翔 刘许成 杨晓光[2] Lindong Liu;Zixiang Wu;Xucheng Liu;Xiaoguang Yang

机构地区：[1]中国科学技术大学管理学院,合肥230026 [2]中国科学院数学与系统科学研究院系统科学研究所,北京100190

出　　处：《中国科学:数学》2025年第2期517-534,共18页Scientia Sinica:Mathematica

基　　金：国家自然科学基金(批准号:72022018和72192800);中国科学院青年创新促进会(批准号:2021454)资助项目。

摘　　要：在数字经济迅速发展的今天,作为其基础理论之一的博弈论正在迎来新的发展机遇.因强调集体理性,故合作博弈在合作竞争等问题中应用广泛.然而,许多合作博弈的核心并不存在,即所谓的非平衡博弈,这导致了大联盟的不稳定.因此,研究非平衡博弈并找到其稳定解对于合作博弈的发展和应用至关重要.本文首先系统梳理了国内外大联盟稳定解的研究进展,并将该领域的研究分为两类,即外部约束松弛角度和内部结构修正角度.进一步地,根据松弛的约束类型,本文将外部约束松弛角度的研究分为两类:松弛预算平衡约束和松弛联盟稳定约束.根据修正的结构类型,将内部结构修正角度的研究分为两类:考虑权限结构限制和考虑系数结构调整.最后,本文分别从理论层面和应用层面分别提出两点研究展望:寻找新的构造大联盟稳定解的方法,解决更具适用性的非平衡博弈实际问题.With the rapid development of the digital economy,game theory,as one of its foundational theories,is encountering new opportunities for development.Due to its emphasis on collective rationality,cooperative game theory is widely applied to issues concerning cooperation.However,many cooperative games’cores are empty,namely,the so-called non-balanced games,which leads to instability in grand coalitions.Therefore,studying non-balanced games and finding their stable solutions is crucial for the development and application of cooperative game theory.In this paper,we first systematically review the research on stable solutions in grand coalitions both domestically and internationally,and categorize the research in this field into two perspectives:relaxation of external constraints and modification of internal structures.Furthermore,based on the types of relaxed constraints,we divide the research from the perspective of relaxation of external constraints into two categories:relaxation of budget balance constraints and relaxation of coalition stability constraints.Regarding the modified structural types,the research from the perspective of modification of internal structures is divided into two categories:considering authority structure restrictions and considering coefficient structure adjustments.Finally,we propose two research prospects from both theoretical and practical perspectives:finding new methods to construct stable solutions in grand coalitions and addressing real-world issues of unbalanced games with stronger applicability.

关 键 词：合作博弈 核心 非平衡博弈 成本分摊 稳定解 

分 类 号：O225[理学—运筹学与控制论]