拟阵上合作对策的单调解

本文主要介绍了拟阵上的合作对策Shapley解的结构,并利用强单调性、交换性、概率有效性等三条公理刻画了拟阵上合作对策Shapley解的唯-性.同时讨论了本文的三条公理与Bilbao等人的四条 公理的等价性.最后给出拟阵上合作对策核心的定义及其结构.     

拟阵上动态结构合作对策的单调解

论文主要介绍了拟阵上动态结构合作对策单调解的结构,并利用强单调性、交换性和动态有效性等三条公理刻画了此单调解的唯一性.同时给出了拟阵上动态结构合作对策核心的定义,确定了它的结构.最后讨论了拟阵上动态结构合作对策Shapley值与其核心的关系.     

拟阵限制下合作对策解的传递性

Vincent Feltkamp研究了Shapley解和Banzhaf解的公理性．Bilbao等人又对拟阵限制下的Shapley解的性质进行了讨论．本文在此基础上主要研究了拟阵限制下的合作对策Shapley解，并利用传递性、交换性、概率有效性和P-哑元性等四条公理证明了拟阵限制下合作对策Shapley解的唯一性．进而证明了拟阵限制条件下简单对策Shapley解的唯一性．最后给出了拟阵限制下合作对策的Banzhaf解的唯一性定理．     

区间值合作对策的广义区间Shapley值

研究区间Shapley值通常对区间值合作对策的特征函数有较多约束,本文研究没有这些约束条件的区间值合作对策,以拓展区间Shapley值的适用范围。首先,本文指出广义H-差在减法与加法运算中存在的问题,进而提出了一种改进的广义H-差,称为扩展的广义H-差。然后,基于扩展的广义H-差,定义了区间值合作对策的广义区间Shapley值,并用区间有效性、区间对称性、区间哑元性和区间可加性等四条公理刻画了该广义区间Shapley值。同时,证明了该值的存在性与唯一性,而且得到了该值的一些性质。研究表明,任意的区间值合作对策的广义区间Shapley值都存在。最后,以算例说明该广义区间Shapley值的可行性与实用性。     

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。     

合作对策的改进Shapley解

本文根据经典合作对策Shapley解的适用范围提出了改进Shapley解,且改进Shapley解更能描述现实生活中的一类经济现象.同时利用与刻画经典合作对策Shapley解类似的几个公理刻画了改进Shapley解.并将改进Shapley解的分配方法应用到了协调利益分配的实例中.     

模糊支付合作博弈的广义Shapley函数

基于广义H-差研究了收益是模糊数的合作博弈的广义Shapley函数。首先,对广义H-差的运算做了合理的假设,并以此为基础,给出了区间值合作博弈的广义区间Shapley值的定义和公理体系。然后,根据模糊数与其截集的关系,给出了模糊支付合作博弈的广义Shapley函数的表达式,并用广义有效性、广义哑元性、广义对称性、广义可加性等四条公理刻画了该广义Shapley函数。同时,给出了广义Shapley函数的存在性条件,证明了广义Shapley函数的存在性与唯一性。并且发现,任意的区间值合作博弈的广义区间Shapley值都存在,任意的收益为中心三角模糊数的合作博弈的广义Shapley函数也都存在。另外,本文指出了不能直接利用α—截集博弈的广义区间Shapley值通过集合套理论构造广义Shapley函数。     

区间合作对策在增广系统上的区间Shapley值

给出了区间合作对策在增广系统上的定义,并利用相应的公理体系及区间数运算的性质,构造出区间合作对策在增广系统上的区间Shapley值,论证了当对策为区间凸对策时的区间Shapley值的唯一性,且探讨了该区间Shapley值的一些性质.最后通过算例来说明在此类区间合作对策上所提方法的实用性与有效性.     

直觉模糊支付合作对策的Shapley值

主要研究支付值是直觉模糊数的合作对策Shapley值的问题.首先在直觉模糊支付合作对策的基础上,定义了直觉模糊支付函数的截集及直觉模糊合作对策的截集分配;其次将经典的Shapley函数满足的三条公理进行拓展,并构造了直觉模糊Shapley值;最后通过一个算例来验证该方法的有效性。     

基于区间与模糊Shapley值的合作收益分配策略

将经典Shapley值三条公理进行拓广,提出具有模糊支付合作对策的Shapley值公理体系。研究一种特殊的模糊支付合作对策,即具有区间支付的合作对策,并且给出了该区间Shapley值形式。根据模糊数和区间数的对应关系,提出模糊支付合作对策的Shapley值,指出该模糊Shapley值是区间支付模糊合作对策的自然模糊延拓。结果表明:对于任意给定置信水平α,若α=1,则模糊Shapley值对应经典合作对策的Shapley值,否则对应具有区间支付合作对策的区间Shapley值。通过模糊数的排序,给出了最优的分配策略。由于对具有模糊支付的合作对策进行比较系统的研究,从而为如何求解局中人参与联盟程度模糊化、支付函数模糊化的合作对策,奠定了一定的基础。     

Compensations in the Shapley value and the compensation solutions for graph games

We consider an alternative expression of the Shapley value that reveals a system of compensations: each player receives an equal share of the worth of each coalition he belongs to, and has to compensate an equal share of the worth of any coalition he does not belong to. We give a representation in terms of formation of the grand coalition according to an ordering of the players and define the corresponding compensation vector. Then, we generalize this idea to cooperative games with a communication graph in order to construct new allocation rules called the compensation solutions. Firstly, we consider cooperative games with arbitrary graphs and construct rooted spanning trees (see Demange, J Political Econ 112:754–778, 2004) instead of orderings of the players by using the classical algorithms DFS and BFS. If the graph is complete, we show that the compensation solutions associated with DFS and BFS coincide with the Shapley value and the equal surplus division respectively. Secondly, we consider cooperative games with a forest (cycle-free graph) and all its rooted spanning trees. The compensation solution is characterized by component efficiency and relative fairness. The latter axiom takes into account the relative position of a player with respect to his component in the communication graph.     

Proof of permutationally convexity of MCSF games

Granot and Huberman (1982) showed that minimum cost spanning tree (MCST) games are permutationally convex (PC). Recently, Rosenthal (1987) gave an extension of MCST games to minimum cost spanning forest (MCSF) games and showed these games have nonempty cores. In this note we show any MCSF game is a PC game.     

On the core of cost-revenue games: Minimum cost spanning tree games with revenues

In this paper, we analyze cost sharing problems arising from a general service by explicitly taking into account the generated revenues. To this cost-revenue sharing problem, we associate a cooperative game with transferable utility, called cost-revenue game. By considering cooperation among the agents using the general service, the value of a coalition is defined as the maximum net revenues that the coalition may obtain by means of cooperation. As a result, a coalition may profit from not allowing all its members to get the service that generates the revenues. We focus on the study of the core of cost-revenue games. Under the assumption that cooperation among the members of the grand coalition grants the use of the service under consideration to all its members, it is shown that a cost-revenue game has a nonempty core for any vector of revenues if, and only if, the dual game of the cost game has a large core. Using this result, we investigate minimum cost spanning tree games with revenues. We show that if every connection cost can take only two values (low or high cost), then, the corresponding minimum cost spanning tree game with revenues has a nonempty core. Furthermore, we provide an example of a minimum cost spanning tree game with revenues with an empty core where every connection cost can take only one of three values (low, medium, or high cost).     

A vertex oriented approach to the equal remaining obligations rule for minimum cost spanning tree situations

In this paper, we consider spanning tree situations, where players want to be connected to a source as cheap as possible. These situations involve the construction of a spanning tree with the minimum cost as well as the allocation of the cost of this minimum cost spanning tree among its users in a fair way. Feltkamp, Muto and Tijs 1994 introduced the equal remaining obligations rule to solve the cost allocation problem in these situations. Recently, it has been shown that the equal remaining obligations rule satisfies many appealing properties and can be obtained with different approaches. In this paper, we provide a new approach to obtain the equal remaining obligations rule. Specifically, we show that the equal remaining obligations rule can be obtained as the average of the cost allocations provided by a vertex oriented construct-and-charge procedure for each order of players.     

Minimum cost spanning tree games

We consider the problem of cost allocation among users of a minimum cost spanning tree network. It is formulated as a cooperative game in characteristic function form, referred to as a minimum cost spanning tree (m.c.s.t.) game. We show that the core of a m.c.s.t. game is never empty. In fact, a point in the core can be read directly from any minimum cost spanning tree graph associated with the problem. For m.c.s.t. games with efficient coalition structures we define and construct m.c.s.t. games on the components of the structure. We show that the core and the nucleolus of the original game are the cartesian products of the cores and the nucleoli, respectively, of the induced games on the components of the efficient coalition structure.This paper is a revision of [4].     

Truth-telling and Nash equilibria in minimum cost spanning tree models

In this paper we consider the minimum cost spanning tree model. We assume that a central planner aims at implementing a minimum cost spanning tree not knowing the true link costs. The central planner sets up a game where agents announce link costs, a tree is chosen and costs are allocated according to the rules of the game. We characterize ways of allocating costs such that true announcements constitute Nash equilibria both in case of full and incomplete information. In particular, we find that the Shapley rule based on the irreducible cost matrix is consistent with truthful announcements while a series of other well-known rules (such as the Bird-rule, Serial Equal Split, and the Proportional rule) are not.     

“Optimistic” weighted Shapley rules in minimum cost spanning tree problems

We introduce optimistic weighted Shapley rules in minimum cost spanning tree problems. We define them as the weighted Shapley values of the optimistic game v⁺ introduced in Bergantiños and Vidal-Puga [Bergantiños, G., Vidal-Puga, J.J., forthcoming. The optimistic TU game in minimum cost spanning tree problems. International Journal of Game Theory. Available from: <http://webs.uvigo.es/gbergant/papers/cstShapley.pdf>]. We prove that they are obligation rules [Tijs, S., Branzei, R., Moretti, S., Norde, H., 2006. Obligation rules for minimum cost spanning tree situations and their monotonicity properties. European Journal of Operational Research 175, 121–134].     

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。