边赋权图对策Myerson值的和分解

An Additive Decomposition of the Myerson Value on Link-weighted Graph Games

2003年,Gómez等在考虑社会网络中心性度量时,引入了对称对策上Myerson值的和分解概念,本文将这一概念推广到边赋权图对策上,给出了相应于边赋权图对策的组内Myerson值和组间Myerson值。其中边的权表示这条边的两个端点之间的直接通讯容量,组内Myerson值衡量了每个参与者来自它所在联盟的收益,而组间Myerson值评估了参与者作为其他参与者中介所获取的收益。本文侧重分析了边赋权图对策的组内Myerson值和组间Myerson值的权稳定性和广义稳定性,并给出了这两类值的刻画。

Gómez et al.(2003)introduced an additive decomposition of Myerson value for symmetric games as centrality measures.Firstly we generalize this decomposition to the link-weighted graph games and propose the within groups Myerson value and the between groups Myerson value on link-weighted graph games.In this paper,we assume that the weights of a link-weighted graph represent the directed capacity between two nodes.One of them,the within groups Myerson value,determines which part corresponds to the profit from the coalitions that a given player is in,whereas the other,the between groups Myerson value,evaluates the rewards obtained by acting as an intermediary among the other players.This paper focuses on the weight stability and generalized stability of above two values based on the totally positive games,meaning that all dividends are nonnegative and we characterize these values by using three axioms,which are“additivity”,“nullplayer property”and“essential player property”.