Sequencing Games with Slack Due Windows and Group Technology Considerations

We study sequencing situations in which the customers are initially sequenced to be served by a single server. We consider both slack due windows and group technology simultaneously. We introduce two division rules to divide among the customers the cost saving from resequencing the customers to follow the optimal sequence and characterize the rules axiomatically. Applying cooperative game theory to analyze the sequencing games corresponding to the sequencing situations, we use the theory’s solution concepts to solve the games.     

Strategic Manipulation Approach for Solving Negotiated Transfer Pricing Problem

This paper suggests an approach for solving the transfer pricing problem, where negotiation between divisions is carried out considering the manipulation game theory model for a multidivisional firm. The manipulation equilibrium point is conceptualized under the Machiavellian social theory, represented by three concepts: views, tactics and immorality. In this approach, we are considering a non-cooperative model for the transfer pricing problem: a game model involving manipulating and manipulated players engaged cooperatively in a Nash game, restricted by a Stackelberg game. The cooperation is represented by the Nash bargaining solution. The transfer pricing problem is conceptualized as a strong Stackelberg game involving manipulating and manipulated divisions. This structure established conditions of unequal relative power among divisions, where high-power divisions tend to be abusive and less powerful divisions have a tendency to behave compliantly. For computation purposes, we transform the Stackelberg game model into a Nash game, where every division is able of manipulative behavior to some degree: the Nash game relaxes the interpretation of the manipulation game and the equilibrium selection for the transfer pricing problem. The manipulation dynamics and rationality proposed for the transfer pricing problem correspond to many real-world negotiation situations. We present an example, that illustrates how manipulation can be employed to solve the transfer pricing problem in a multidivisional firm.     

The interval Shapley value: an axiomatization

The Shapley value, one of the most widespread concepts in operations Research applications of cooperative game theory, was defined and axiomatically characterized in different game-theoretic models. Recently much research work has been done in order to extend OR models and methods, in particular cooperative game theory, for situations with interval data. This paper focuses on the Shapley value for cooperative games where the set of players is finite and the coalition values are compact intervals of real numbers. The interval Shapley value is characterized with the aid of the properties of additivity, efficiency, symmetry and dummy player, which are straightforward generalizations of the corresponding properties in the classical cooperative game theory.     

模糊支付合作博弈的可信性准核仁

合作博弈是处理局中人之间协同行为的数学理论。有诸如核心、稳定集、沙普利值、准核仁和核仁等不同的解概念。在很多情形,除了借助专家经验和主观直觉,没有恰当的方式来确定支付函数,由此产生了具有模糊支付的合作博弈模型。准核仁是一种重要的解概念,在模糊支付合作博弈中如何恰当定义准核仁是个重要的问题。本文在可信性理论的框架下研究了这个问题,定义了两类可信性准核仁概念并证明了它们的存在性和唯一性,同时研究了可信性核心、可信性核仁与它们之间的关系。     

最小费用k度限制树对策

本在Glover—Klingman算法及最小费用支撑树对策的基础上，讨论了最小费用k度限制树对策问题．利用威胁、旁支付理论制订了两种规则，并利用优超、策略等价理论分别给出了在这两种规则下最小费用k度限制树对策核心中的解，从而证明了在这两种规则下其核心非空．     

A game theoretical model of DEA efficiency

Motivated by the inherent competitive nature of the DEA efficiency assessment process, some effort has been made to relate DEA models to game theory. Game theory is considered not only a more natural source of representing competitive situations, but also beneficial in revealing additional insights into practical efficiency analysis. Past studies are limited to connecting efficiency games to some particular versions of DEA models. The generalised DEA model considered in this study unifies various important DEA models and presents a basic formulation for the DEA family. By introducing a generalised convex cone constrained efficiency game model in assembling the generalised DEA model, a rigorous connection between game theory and the DEA family is established. We prove the existence of optimal strategies in the generalised efficiency game. We show the equivalence between game efficiency and DEA efficiency. We also provide convex programming models for determination of the optimal strategies of the proposed games, and show that the game efficiency unit corresponds to the non-dominated solution in its corresponding multi-objective programming problem. Our study largely extends the latest developments in this area. The significance of such an extension is for research and applications of both game theory and DEA.     

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.     

阈值风险下的多企业合作治理污染的演化博弈分析

针对环境污染具有跨区域性,环境资源的公共物品属性,由单一产污企业治理污染物难以取得有效成果,辖区内多个产污企业合作治理是环境保护的必由之路。 本文从演化博弈论的研究视角探讨了多个排污企业之间的决策演化过程,建立了多主体演化博弈模型,并考虑了污染排放总量超过总量阈值时的环境恶化风险,研究阈值风险对产污企业合作治理污染策略选择的影响。 研究结果表明,较高的治理成本很大地约束了逐利企业治理污染的行为选择,造成公地悲剧的社会问题。 企业治污成本较大背景下,环境阈值风险发生概率越高,越能有效促进合作治理环境策略的演化稳定,合作治理占优于不治理。 出于对企业自身初始禀赋的保护,产污企业初始禀赋越大、排污收费率越高,越能有效促进企业治理污染物的积极性。 最后,为促进辖区内污染企业合作治理污染提出了政策建议。     

<Emphasis Type="Italic">n</Emphasis>-Person Second-Order Games: A Paradigm Shift in Game Theory

In this paper, we present a new approach to n-person games based on the Habitual domain theory. Unlike the traditional game theory models, the constructed model captures the fact that the underlying changes in the psychological aspects and mind states of the players over the arriving events are the key factors, which determine the dynamic process of coalition formation. We introduce two new concepts of solution for games: strategically stable mind profile and structurally stable mind profile. The theory introduced in this paper overcomes the dichotomy of non-cooperative/cooperative games, prevailing in the existing game theory, which makes game theory more applicable to real-world game situations.     

A cost allocation problem in urban solid wastes collection and disposal

In this paper we consider a cost allocation problem arising in a consortium for urban solid wastes collection and disposal. A classical allocation rule is the proportional division according to the volume of wastes collected; here we propose a different allocation method, rooted in game theory, based on a model developed by Fragnelli et al. [3], using the Shapley Value and the Owen Value as allocation rules. The model was applied to the data of the consortium Ovadese – Valle Scrivia, comparing our results and the actual ones.     

Opportune moment strategies for a cost spanning tree game

Cost spanning tree problems concern the construction of a tree which provides a connection with the source for every node of the network. In this paper, we address cost sharing problems associated to these situations when the agents located at the nodes act in a non-cooperative way. A class of strategies is proposed which produce minimum cost spanning trees and, at the same time, are strong Nash equilibria for a non-cooperative game associated to the problem. They are also subgame perfect Nash equilibria.     

A project game for PERT networks

An important topic in PERT networks is how to allocate the total expedition (or delay) for situations in which the project is not executed as planned. In order to do that we define a TU project game that satisfies some desirable properties from the management project and game theory point of view.     

A non-cooperative approach to the cost spanning tree problem

We associate to each cost spanning tree problem a non-cooperative game, which is inspired by a real-life problem. We study the Nash equilibria and subgame perfect Nash equilibria of this game. We prove that these equilibria are closely related with situations where agents connect sequentially to the source.Finicial support from the Ministerio de Ciencia y Tecnologia and FEDER, and Xunta de Galicia through grants BEC2002-04102-C02-01 and PGIDIT03PXIC30002PN is gratefully acknowledged.     

知识创造行为与组织惯例的演化博弈及其仿真研究

以演化博弈模型为主要理论工具,在对知识创造行为与组织惯例关系予以描述的基础上,构建知识创造行为与组织惯例的演化博弈模型。通过求解复制动态方程,分析不同条件下知识创造行为与组织惯例分别达到演化稳定均衡的策略。研究结果表明:知识创造行为与组织惯例的匹配属于动态、重复博弈过程,参与博弈的预期收益、激励成本、转换成本直接决定演化稳定策略且影响个体对知识创造行为与组织惯例的选择,知识创造行为则倾向以承袭为主的保守策略。演化博弈方法的引入为知识创造行为和组织惯例的研究开辟了全新视角,也为相关领域的进一步探索提供有利的理论支持。     

Nash equilibria in all-optical networks

We consider the problem of routing a number of communication requests in WDM (wavelength division multiplexing) all-optical networks from the standpoint of game theory. If we view each routing request (pair of source-target nodes) as a player, then a strategy consists of a path from the source to the target and a frequency (color). To reflect the restriction that two requests must not use the same frequency on the same edge, conflicting strategies are assigned a prohibitively high cost.Under this formulation, we consider several natural cost functions, each one reflecting a different aspect of restriction in the available bandwidth. For each cost function we examine the problem of the existence of pure Nash equilibria, the complexity of recognizing and computing them and finally, the problem in which we are given a Nash equilibrium and we are asked to find a better one in the sense that the total bandwidth used is less. As it turns out some of these problems are tractable and others are NP-hard.     

Second-order game problem: Decision dynamics in gaming phenomena

The paradigm of decision dynamics (Ref. 1) is used to describe the decision dynamics involving more than one decision-maker. The framework supplied in this paper is different from traditional game theory or differential games. Traditional simplicity assumptions are replaced by a more complicated, but more realistic, setting. Although many mathematically beautiful results in traditional game theory or differential games have disappeared in second-order games, the more realistic setting of the latter does make it easier for the decision-makers to find agood decision. Concepts of time optimality and time stability, and their necessary and/or sufficient conditions are described. Unconventional concepts of strategies and uncertainty involved in gaming phenomena are discussed. A highlight of the paper is a systematic discussion on reframing tactics of gaming situations, which do not exist in the context of traditional game theory or differential games. Various research topics are discussed at the end of the paper.     

Cooperative interval games: a survey

The (re)distribution of collective gains and costs is a central question for individuals and organizations contemplating cooperation under uncertainty. The theory of cooperative interval games provides a new game theoretical angle and suitable tools for answering this question. This survey aims to briefly present the state-of-the-art in this young field of research, discusses how the model of cooperative interval games extends the cooperative game theory literature, and reviews its existing and potential applications in economic and operations research situations with interval data.     

Onn-person noncooperative multicriteria games described in strategic form

This paper undertakes the problem of multicriteria decision support in conflict situations described as a noncooperative game. Construction of such a decision support requires the development of the noncooperative game theory to be generalized for the multicriteria case. New theoretical results in this case are presented. Features of the multicriteria noncooperative games are shown with use of a duopoly model in case of two goods and two criteria of each player. Concepts of the decision support are discussed.     

基于进化博弈视角的水源地与下游生态补偿合作演化分析

水源地与下游地方政府之间的协议合作可以协调流域上下游之间的矛盾和利益,是一种可实现流域生态保护良性循环的生态补偿尝试。本文应用进化博弈的双种群博弈理论,研究了水源地和下游地方政府之间博弈演化过程及影响因素。研究表明,流域上下游地方政府合作的演化方向主要受水源地不保护及下游不补偿受到的惩罚、下游对水源地的补偿额度、水源地和下游合作的初始成本、水源地生态保护的成本及收益等八个因素的影响。降低水源地的保护成本及水源地和下游合作的初始成本,提高水源地因保护而获得的综合效益、提高水源地不保护及下游不补偿受到的惩罚额度、合理确定下游对水源地的补偿额度将有利于水源地生态补偿机制向合作方向演进。     

基于累积前景理论的联盟企业知识转移演化博弈分析

知识转移过程是一个复杂的博弈过程,演化博弈论可以很好地解释转移主体行为。考虑到传统的演化博弈模型不能对知识转移主体非理性心理因素及风险偏好问题进行有效解释,本文将累积前景理论与演化博弈相结合,运用前景价值函数完善支付矩阵的部分参数,分析博弈模型的演化稳定策略。通过仿真模拟得出如下结论:知识转移存在两个演化稳定策略;转移策略由直接收益、转移成本及前景损益等因素决定;转移方的风险损失对转移策略影响较大,而接收方潜在收入对知识转移策略影响较小。