具有超图合作结构的赋权Position值

具有超图交流结构的可转移效用合作对策,也称为超图对策,它由一个三元组(N,v,H)所组成,其中(N,H)是一个可转移效用对策(简称TU-对策),而(N,H)是一个超图(超网络)。在超图对策中,除Myerson值(Myerson)外,Position值(Meessen)是另一个重要的分配规则。该模型要求把超图结构中每条超边Shapley的值平均分配给它所包含的点,而不考虑每个点的交流能力或合作水平。本文引入超图结构中点的度值来度量每条超边中每个点的交流能力或合作水平,并结合Haeringer提出用于推广Shapley值的权重系统,并由此定义了具有超图合作结构的赋权Position值。我们证明了具有超图合作结构的赋权Position值可以由“分支有效性”、“冗余超边性”、“超边可分解性”、“拟可加性”、“弱积极性”和“弱能转换”六个性质所唯一确定,并且发现参与者获得的支付随其度值的增加而增加,参与者分摊的成本随其度值的增加而降低。     

超网络博弈的位置值的公理化刻画

在图博弈中,Myerson假设只有连通的联盟才能获得完全的效用,而忽略连通联盟的具体结构.1996年,Jackson和Wolinsky提出了“网络情形博弈”的模型,拓展了Myerson的图博弈模型.它是利用值函数代替原来的特征函数以体现不同网络结构对合作结果的影响.考虑超网络情形博弈,它是网络情形博弈的自然推广,由三元组（N,H,v）所组成,这里v是值函数,用于描述在超网络（N,H）合作结构下的合作收益.2012年,van den Nouweland和Slikker利用四个公理给出了位置值的公理化刻画.通过分支有效性和局部平衡超边贡献性两个公理,给出了超网络博弈中位置值的公理化刻画.作为推论,得到了网络博弈中位置值的新刻画.     

有效商Myerson值的公理化刻画

在具有图结构的合作对策中，Myerson值(Myerson, 1977)是一个著名的分配规则，它可以由分支有效性和公平性或者平衡贡献性所唯一确定。在实际中，图结构可能并不影响大联盟的形成，只是由于参与者在网络中所处的位置不同，对其讨价还价能力会产生影响。换句话说，图结构会对分配格局产生影响，但对大联盟的形成没有影响。这促使人们开始考虑Myerson值的有效推广问题。文献中已经提出了Myerson的几种有效推广形式。2020年，Li和Shan提出了有效商Myerson值并给出了公理化刻画，它是Myerson值一种新的有效推广形式。本文首先引入了准商盈余公平性这一性质，然后结合有效性和Myerson值黏性给出了有效商Myerson值的新公理化刻画。其次，通过应用案例，将该值和其他值做了比较分析。     

边赋权图对策Myerson值的和分解

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。     

图上合作博弈和图的边密度

1977年, Myerson建立了以图作为合作结构的可转移效用博弈模型(也称图博弈), 并提出了一个分配规则, 也即"Myerson 值", 它推广了著名的Shapley值. 该模型假定每个连通集合(通过边直接或间接内部相连的参与者集合)才能形成可行的合作联盟而取得相应的收益, 而不考虑连通集合的具体结构. 引入图的局部边密度来度量每个连通集合中各成员之间联系的紧密程度, 即以该连通集合的导出子图的边密度来作为他们的收益系数, 并由此定义了具有边密度的Myerson值, 证明了具有边密度的Myerson值可以由"边密度分支有效性"和"公平性"来唯一确定.     

联盟缺额合意性与均分不可分贡献值

文章首先基于联盟盈余合意性(Hu,2019)提出了合作博弈解新的公理,即联盟缺额合意性,并证明了除了不超过2个局中人合作博弈的平凡情形之外,联盟缺额合意性与合作博弈解的有效性互斥.其次,通过对联盟缺额进行平均化引入了平均联盟缺额合意性,进一步结合有效性和可加性实现了均分不可分贡献值的公理化刻画.最后,将相关公理化结果拓展到了权重均分不可分贡献值(Hou等,2019).     

超网络中心性度量的υ-Position值方法

利用合作博弈理论的分配规则如Shapley值、Banzhaf值等来度量政治、经济和社会网络中节点的中心性或者重要性是识别网络中关键节点的一类重要方法。考虑到在超网络中代表各类组织的超边在网络中发挥的作用不同,本文研究了超网络博弈上一类广义Position值的分配规则,被称为υ-position值。它可以作为网络中度值测度的一类推广,以此来度量网络中参与者的中心性和相对重要性。其次,证明了超网络结构上类Shapley-position值可由分支超边指数和局部平衡超边贡献两个性质所唯一刻画。最后, 举例分析了υ-position值在超网络中心性测度中的应用。     

有限合作博弈的Shapley分配

以Myerson关于有限合作的图博弈模型为基础,结合经典合作博弈的相关结论,建立了有限合作博弈的Shapley分配,讨论了分配的相关性质.同时在支付函数满足链递增性的假设下,进一步研究了有限合作关系变化对收益分配的影响,给出了相关的研究结论.     

求解一类直觉模糊联盟合作博弈Shapley值的新方法北大核心CSCD

文章对带有Choquet积分的直觉模糊联盟合作博弈Shapley值进行了研究.通过证明一类直觉模糊联盟合作博弈Shapley值满足单调性条件,给出该类直觉模糊联盟合作博弈Shapley值的简单计算方法.该方法是由区间特征函数的上下界直接计算得出直觉模糊联盟合作博弈Shapley值的上下界,避免了区间数减法.此外,文章又进一步对该类直觉模糊联盟合作博弈Shapley值的性质进行了证明.最后通过数值实例说明该方法的适用性和有效性.     

带层次结构效用可转移合作对策的collective值

层次结构是比联盟结构更一般化的结盟限制形式.文章给出了带层次结构效用可转移合作对策collective值的两种定义.第一种类似于带层次结构效用可转移合作对策的ζ值,从多步分配的角度定义了collective值;第二种类似于带图结构效用可转移合作对策的Myerson值,从交流限制的角度定义了collective值.文中证明了这两种定义是等价的,并给出了collective值的一个公理化刻画.研究结果丰富了带层次结构效用可转移合作对策的解概念,可为研究其它带结盟限制效用可转移合作对策的值函数提供借鉴.     

The Myerson value for directed graph games

A directed graph game consists of a cooperative game with transferable utility and a digraph which describes limited cooperation and the dominance relation among the players. Under the assumption that only coalitions of strongly connected players are able to fully cooperate, we introduce the digraph-restricted game in which a non-strongly connected coalition can only realize the sum of the worths of its strong components. The Myerson value for directed graph games is defined as the Shapley value of the digraph-restricted game. We establish axiomatic characterizations of the Myerson value for directed graph games by strong component efficiency and either fairness or bi-fairness.     

The degree value for games with communication structure

A new value concept, called degree value, is proposed by employing the degree game induced by an original game for hypergraph communication situations (including graph communication situations). We provide an axiomatic characterization of the degree value for arbitrary hypergraph communication situations by applying component efficiency and balanced conference contributions, which is a natural extension of balanced link contributions introduced in Slikker (Int J Game Theory 33:505–514, 2005) for graph communication situations. By comparing the degree value with the position value and the Myerson value, it is verified that the degree value is a new allocation rule that differs from both the Myerson value and the position value, and the degree value highlights the important role of the degree of a player in hypergraph communication situations. Particularly, in a uniform hypergraph communication situation, where every conference contains the same number of players, we show that the degree value coincides with the position value.     

Games with externalities: games in coalition configuration function form

In this paper we introduce a model of cooperative game with externalities which generalizes games in partition function form by allowing players to take part in more than one coalition. We provide an extension of the Shapley value (1953) to these games, which is a generalization of the Myerson value (1977) for games in partition function form. This value is derived by considering an adaptation of an axiomatic characterization of the Myerson value (1977).     

The core and the Weber set of games on augmenting systems

This paper deals with cooperative games in which only certain coalitions are allowed to form. There have been previous models developed to confront the problem of unallowable coalitions. Games restricted by a communication graph were introduced by Myerson and Owen. In their model, the feasible coalitions are those that induce connected subgraphs. Another type of model is introduced in Gilles, Owen and van den Brink. In their model, the possibilities of coalition formation are determined by the positions of the players in a so-called permission structure. Faigle proposed a general model for cooperative games defined on lattice structures. In this paper, the restrictions to the cooperation are given by a combinatorial structure called augmenting system which generalizes antimatroid structure and the system of connected subgraphs of a graph. In this framework, the core and the Weber set of games on augmenting systems are introduced and it is proved that monotone convex games have a non-empty core. Moreover, we obtain a characterization of the convexity of these games in terms of the core of the game and the Weber set of the extended game.     

基于图对策的收益分配

基于具有交流结构的合作对策,即图对策,对平均树解拓展形式的特征进行刻画,提出此解满足可加性公理。进一步地,分析了对于无圈图对策此解是分支有效的。并且当连通分支中两个局中人相关联的边删掉后,此连通分支的收益变化情况可用平均树解表示。这一性质是Shapley值和Myerson值所不具有的。最后,我们给出了模糊联盟图对策中模糊平均树解的可加性和分支有效性。     

Axiomatizations of the Shapley value for games on augmenting systems

This paper deals with cooperative games in which only certain coalitions are allowed to form. There have been previous models developed to confront the problem of unallowable coalitions. Games restricted by a communication graph were introduced by Myerson and Owen. In their model, the feasible coalitions are those that induce connected subgraphs. Another type of model is introduced in Gilles, Owen and van den Brink. In their model, the possibilities of coalition formation are determined by the positions of the players in a so-called permission structure. Faigle proposed another model for cooperative games defined on lattice structures. We introduce a combinatorial structure called augmenting system which is a generalization of the antimatroid structure and the system of connected subgraphs of a graph. In this framework, the Shapley value of games on augmenting systems is introduced and two axiomatizations of this value are showed.