均衡博弈的核心妥协解及其公理化  

The core compromise solution for balanced games and its axiomatization

作　　者：宫豆豆 徐根玖[2] GONG Doudou;XU Genjiu(School of Economics and Management,Nanjing University of Science and Technology,Nanjing 210094,China;School of Mathematics and Statistics,Northwestern Polytechnical University,Xi’an 710072,China)

机构地区：[1]南京理工大学经济管理学院,南京210094 [2]西北工业大学数学与统计学院,西安710072

出　　处：《系统工程理论与实践》2024年第4期1210-1218,共9页Systems Engineering-Theory & Practice

基　　金：国家重点研发计划(2021YFA1000402);国家自然科学基金(72071159);南京理工大学智库专项(2023CG002)。

摘　　要：效用可转移的均衡博弈的核心刻画了参与人形成稳定的合作后收益的分配方式.以参与人合作形成前后所得到的最少支付和最大支付为参考点,本文定义了参与人的最小权力向量和最大权力向量,然后将这两个向量的唯一有效妥协定义为一个新的解,称为核心妥协解.本文分析了均衡博弈的核心妥协解与另一个著名妥协解τ-值以及核心之间的关系.基于最小权力优先性和零规范情形最大权力比例性,公理化刻画了均衡博弈的核心妥协解.将最小权力优先性替换为策略均衡不变性,本文给出了核心妥协解的另一个公理化刻画.最后,以机场跑道成本分摊为例,分析了核心妥协解的应用.The core for balanced games with transferable utility characterizes all the allocations of payoffs when players solidly cooperate.Taking the minimal and maximal payoffs received by the players before and after the formation of cooperation respectively as reference points,this paper defines the vectors of minimal and maximal rights of the players,and further defines the unique efficient compromise of these two vectors as a new solution,called the core compromise solution.This paper analyses the relation among the core compromise solution,the τ-value and the core for balanced games,where the τ-value is another well-known compromise solution.This paper axiomatically characterizes the core compromise solution with the minimal rights priority property and the zero-normalized maximal rights proportionality property.Replacing the minimal rights priority property as the relatively invariance with respect to strategic equivalence,this paper provides another axiomatic characterization of the core compromise solution.Finally,this paper analyses the application of the core compromise solution,taking airport runway cost allocation as an example.

关 键 词：均衡博弈 核心 妥协解 公理化 

分 类 号：O225[理学—运筹学与控制论] F224.32[理学—数学]