合作博弈的比例分离解及其在区域经济一体化中的应用

文章对合作博弈理论进行了研究,结合比例分配以及联盟形成过程,提出了比例分离解的概念.该解首先利用给定权重,基于回报率递减划分大联盟,得到了大联盟的适配划分,随后由适配划分确定的加入顺序对划分联盟的边际贡献按比例分配.然后,基于最高回报一致性对比例分离解的公理刻画进行了研究,得到了3个刻画定理.最后,将新的解概念应用到区域经济一体化问题中,建立了经济协同博弈模型,并以长三角地区为例,分析了该区域经济协同发展的贡献情况和发展规划.     

易腐品供应链企业联合采购决策与费用分配研究

在激烈的市场竞争中,如何降低成本以及保证产品的新鲜度对于销售易腐性产品的零售商来说具有至关重要的意义.企业间通过实施联合采购可以降低采购成本,增加与供应商的谈判议价能力,因此联合采购受到越来越多的企业以及学者的关注.考虑了在非瞬时补货情况下多零售商向同一供应商联合采购某种易腐品的订货决策及费用分配问题.以易腐品联合采购过程中产生的订货费用作为分配的对象,应用合作博弈理论,将非瞬时补货情况下易腐品联合采购的费用分配问题构造成易腐品的联合采购博弈,证明了该博弈的核心非空且为子模博弈,并给出了核心中的一个分配方案,同时还讨论了补货速率对零售商分担的订货费用的影响.论文最后对几种典型的比例分配解的效率进行了模拟分析.     

具有限制结盟结构的供应链合作创新及其收益分配

针对具有限制结盟结构特征的三级供应链合作创新联盟问题,分析了由单个供应商、制造商和销售商组成的不同联盟系统下的收益情况,并运用图合作博弈的average tree solution(简称“A-T解”)法对各成员的收益进行了分配。结果表明,所有成员参与供应链联盟时总收益最大,且A-T解分配法与Shapley值法相比更具合理性和有效性,能充分突出成员在合作联盟中的特殊地位(位置)及其重要性,该结论进一步通过比较不同级别结构下的供应链收益分配问题进行说明。     

具有限制结盟结构的供应链合作创新及其收益分配

针对具有限制结盟结构特征的三级供应链合作创新联盟问题,分析了由单个供应商、制造商和销售商组成的不同联盟系统下的收益情况,并运用图合作博弈的average tree solution(简称“A-T解”)法对各成员的收益进行了分配。结果表明,所有成员参与供应链联盟时总收益最大,且A-T解分配法与Shapley值法相比更具合理性和有效性,能充分突出成员在合作联盟中的特殊地位(位置)及其重要性,该结论进一步通过比较不同级别结构下的供应链收益分配问题进行说明。     

加权均值方差准则下的最优资本分配

本文考虑相依风险情形下的最优资本分配问题.采用随机加权损失函数,在期望-方差准则下,研究最优资本分配解的存在性,分析加权随机变量选取.进一步,文章提出了以破产概率作为模型评价标准,采用随机模拟的方法分别求解不同模型最优资本分配和相应的破产概率,对模型做出评价.最后,在假设相依风险分别为多元正态分布和多元t分布的情形下,用数值模拟的方法对本文提出的加权期望-方差模型与Dhaene提出的加权均值模型和XU和MAO提出的尾部均值方差模型进行比较,结果显示在破产概率准则下,本文提出的加权期望-方差模型所给出的资金分配比例显著优于其他模型.     

虚拟组织收益分配的博弈分析

运用博弈分析的方法,对虚拟组织的收益分配问题进行了深入的研究,指出了绝对收益分配差距对合作伙伴总收益的影响,阐述了虚拟组织动态博弈条件下,收益分配应满足的条件,论证了按投入比例分配收益的不利影响,以及均分投入与收益的不现实,提出了全面认识弱势合作伙伴投入的价值,打破按投入比例分配收益对虚拟组织的意义.     

保险风险分配的随机合作博弈模型

本文对Suijs和Borm等所建立的模型稍作引伸,并将之应用于保险交易过程中有关各方面的风险分担,在所建立的带有随机支付的保险合作博弈模型框架下,讨论了保险博弈问题可能的结盟方式及其解的概念,并给出了保险风险分配、可行保险风险分配和帕累托最优保险风险分配的定义与形式,最后以实例说明其合理性,研究表明,带有随机支付的保险合作博弈模型能够较好的刻画保险机制的本质。     

基于线性规划博弈的供应链配送问题

着重建立了供应链配送问题的线性规划模型,分析说明了配送合作联盟对各成员是有利的.在配送博弈中,根据配送问题的对偶最优解和配送博弈核心之间的关系,构造了收益分配函数并证明了配送博弈的核心非空、所对应的分配方案稳定等性质.最后通过算例应用验证了模型和分配函数的有效性.     

生态工业链定价策略的博弈分析

生态工业链与传统供应链不同，传统供应链中的定价策略在生态工业链中不再适用。为了解决该问题，基于单一上游企业和单一下游企业构成的生态供应链系统，应用博弈理论对上游企业生产产品时产生的副产品或者废物定价策略进行研究。分别得出了一个非合作博弈的均衡解（斯坦克尔伯格均衡）和一个合作博弈的均衡解（联合定价），并进一步对各种定价策略的效率进行了分析。最后对原料短缺时的定价情况进行了讨论。     

基于平均树值的无圈图博弈有效解

本文对无圈图博弈进行了研究,考虑了大联盟收益不小于各分支收益之和的情况。通过引入剩余公平分配性质,也就是任意两个分支联盟的平均支付变化相等,给出了一个基于平均树值的无圈图博弈有效解。同时,结合有效性和分支公平性对该有效解进行了刻画。特别地,若无圈图博弈满足超可加性时,证明了该有效解一定是核中的元素,说明此时的解是稳定的。最后,通过一案例分析了该有效解的特点,即越大的分支分得的剩余越多,并且关键参与者,也就是具有较大度的参与者可获得相对多的支付。     

Multi-issue allocation situations

This paper introduces a new class of transferable utility games, called multi-issue allocation games. These games arise from various allocation situations and are based on the concepts underlying the bankruptcy model, as introduced by O'Neill [Math. Social Sci. 2 (1982) 345]. In this model, a perfectly divisible good (estate) has to be divided amongst a given set of agents, each of whom has some claim on the estate. Contrary to the standard bankruptcy model, the current model deals with situations in which the agents' claims are multi-dimensional, where the dimensions correspond to various issues.It is shown that the class of multi-issue allocation games coincides with the class of (non-negative) exact games. The run-to-the-bank rule is introduced as a solution for multi-issue allocation situations and turns out to be Shapley value of the corresponding game. Finally, this run-to-the-bank rule is characterised by means of a consistency property in the spirit of O'Neill.     

Parameterized fairness axioms on cycle-free graph games

We study cooperative transferable utility games with a communication structure represented by an undirected graph, i.e., a group of players can cooperate only if they are connected on the graph. This type of games is called graph games and the best-known solution for them is the Myerson value, which is characterized by the component efficiency axiom and the fairness axiom. Recently the average tree solution has been proposed on cycle-free graph games, and shown to be characterized by the component efficiency axiom and the component fairness axiom. We propose e{\epsilon} -parameterized fairness axiom on cycle-free graph games that incorporates the preceding fairness axioms, and show the existence and the uniqueness of the solution. We then discuss a relationship between the existing and our proposed solutions by a numerical example.     

A noncooperative approach to bankruptcy problems with an endogenous estate

We introduce a new class of bankruptcy problems in which the value of the estate is endogenous and depends on agents’ investment decisions. There are two investment alternatives: investing in a company (risky asset) and depositing money into a savings account (risk-free asset). Bankruptcy is possible only for the risky asset. We define a game between agents each of which aims to maximize his expected payoff by choosing an investment alternative and a company management which aims to maximize profits by choosing a bankruptcy rule. Our agents are differentiated by their incomes. We consider three most prominent bankruptcy rules in our base model: the proportional rule, the constrained equal awards rule and the constrained equal losses rule. We show that only the proportional rule is a part of any pure strategy subgame perfect Nash equilibrium. This result is robust to changes in income distribution in the economy and can be extended to a larger set of bankruptcy rules and multiple types. However, extension to multiple company framework with competition leads to equilibria where the noncooperative support for the proportional rule disappears.     

Bankruptcy games

Bankruptcy problems are considered from a game theoretic point of view. Solution concepts from cooperative game theory are studied for bankruptcy games. A necessary and sufficient condition for a division rule for bankruptcy problems to be a game theoretic rule is given. A new division rule which is an adjustment of the proportional rule is given. This rule coincides with theT-value for bankruptcy games. Properties of the new rule are treated and a set of characterizing properties is given.

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Zusammenfassung In dieser Arbeit werden Bankrottprobleme von spieltheoretischer Warte aus behandelt; insbesondere werden Lösungskonzepte der kooperativen Spieltheorie für Bankrottspiele untersucht. Eine notwendige und hinreichende Bedingung wird angegeben dafür, Daß eine Aufteilungsregel für Bankrottprobleme spieltheoretischer Natur ist. Ferner wird eine neue Aufteilungsregel angegeben, welche eine passende Modellierung der Proportionalitätsregel ist. Diese Regel fällt mit dem-Wert für Bankrottspiele zusammen. Schließlich werden Eigenschaften dieser neuen Regel untersucht und eine Axiomatisierung angegeben.

     

The Constrained Equal Awards Rule for Bankruptcy Problems with a Priori Unions

In this paper, we provide two extensions of the constrained equal awards rule for bankruptcy situations to the class of bankruptcy situations with a priori unions. We present some characterisations and relations with corresponding games. The two new extensions are illustrated by a specific application.     

Stochastic bankruptcy games

We study bankruptcy problems where the estate and the claims have stochastic values and we allow these values to be correlated. We associate a transferable utility game with uncertainty to a stochastic bankruptcy problem and use the Weak Sequential Core as a solution concept for such games. We test the stability of a number of well known division rules in this stochastic setting and find that all of them are unstable, with the exception of the stochastic extension of the Constrained Equal Awards rule which leads to a Weak Sequential Core element.     

Two Approaches to the Problem of Sharing Delay Costs in Joint Projects

This paper concentrates on cost sharing situations which arise when delayed joint projects involve joint delay costs. The problem here is to determine fair shares for each of the agents who contribute to the delay of the project such that the total delay cost is cleared. We focus on the evaluation of the responsibility of each agent in delaying the project based on the activity graph representation of the project and then on solving the important problem of the delay cost sharing among the agents involved. Two approaches, both rooted in cooperative game theory methods are presented as possible solutions. In the first approach delay cost sharing rules are introduced which are based on the delay of the project and on the individual delays of the agents who perform activities. This approach is inspired by the bankruptcy and taxation literature and leads to five rules: the (truncated) proportional rule, the (truncated) constrained equal reduction rule and the constrained equal contribution rule. By introducing two coalitional games related to delay cost sharing problems, which we call the pessimistic delay game and the optimistic delay game, also game theoretical solutions as the Shapley value, the nucleolus and the -value generate delay cost sharing rules. In the second approach the delays of the relevant paths in the activity graph together with the delay of the project play a role. A two-stage solution is proposed. The first stage can be seen as a game between paths, where the delay cost of the project has to be allocated to the paths. Here serial cost sharing methods play a role. In the second stage the allocated costs of each path are divided proportionally to the individual delays among the activities in the path.     

Bankruptcy and the per capita nucleolus: The claim-and-right rules family

This article describes the per capita nucleolus for bankruptcy games as a bankruptcy rule. This rule, called the clights rule, is based on the well-known constrained equal awards principle and it takes into account a vector of clights, a new term which is a blend of claims and rights. These clights only depend on the vector of claims while the height of the estate determines whether the clights should be interpreted as modified claims or as rights. It is shown that both the clights rule and the Aumann–Maschler rule can be captured within the family of so-called claim-and-right rules.     

具有联盟结构的position值

position值是图对策中著名的分支有效解, 该值充分体现了图的边在合作中的贡献, 因而也可作为网络中心性的一种测度方法。本文基于van den Brink等提出的具有联盟结构与图结构的合作对策, 将position值推广到具有联盟结构的图对策上, 提出了具有联盟结构的position值, 该值可以作为受优先联盟约束的网络中心性的一种测度方法。本文首先证明了具有联盟结构的position值可以由分割分支有效性和平衡边贡献性所唯一刻画。其次, 以跨国天然气管道网的收益分配为例, 对这个值与其他值做了比较分析。