一种要素双模糊的限制交流结构合作博弈方法及应用

针对具有限制交流结构的合作博弈,基于现实结盟局中人参与联盟程度模糊且联盟支付模糊的情形,提出一种带局中人偏好的要素(联盟与支付)双模糊限制交流结构合作博弈的A-T解(average tree solution)分配方法.首先基于局中人的风险偏好均值,结合模糊联盟合作博弈的Choquet积分形式,构建要素双模糊合作联盟的...     

具有区间模糊联盟的带风险偏好图合作对策A-T解

当前模糊合作对策研究主要基于局中人无差异且联盟组建无约束假设,但现实联盟组建普遍具有限制约束性.针对具有限制交流结构的模糊联盟合作问题,考虑局中人具有不同的偏好差异,提出一种基于风险偏好均值的模糊联盟图合作对策及其A-T解,并公理化论证解的存在性.考虑风险偏好不仅可以体现局中人行为差异性,而且利于模糊联盟支付函数求解.最后通过实例表明了所提出方法的现实有效性和可行性.     

基于CIS值的非合作-合作两型博弈的理论研究

针对Brandenburger和Stuart提出的非合作-合作两型博弈中的不足,提出一种基于转归集中心值(CIS值)的非合作-合作两型博弈理论框架.用CIS值作为合作博弈阶段的解,进而构造获得非合作博弈阶段的纯策略纳什均衡解,并证明该类两型博弈解存在的条件.所提出的非合作-合作两型博弈的求解方法降低了非合作-合作两型博弈的解和有效策略存在的要求,适合于联盟外局中人的策略对联盟具有外部影响时的非合作-合作两型博弈问题,使非合作-合作两型博弈模型的应用更具有一般化,为供应链管理等问题提供新的理论依据.最后,通过数值实例表明所提出模型和方法的有效性和实用性.     

联盟值为梯形模糊数的合作对策最小平方求解模型与方法

针对现实经济管理决策环境与条件具有模糊性的特点,着重研究一类联盟特征(或支付)值为梯形模糊数的合作对策,提出一种求解梯形模糊数合作对策的最小平方优化方法.利用梯形模糊数距离(平方)概念和最小平方法,建立最小化局中人联盟分配和支付值差值平方和的优化模型,根据模型推导出联盟成员梯形模糊数分配值的解析公式,探讨该最小平方解的重要性质.设计一种新的理论优化模型以避免传统梯形模糊数减法导致的计算结果不确定性扩大等问题,为求解梯形模糊数合作对策提供一种新的实践工具与参考思路.     

基于个人超出值的区间值合作博弈新的求解模型

从个人超出值的视角研究特征函数为区间值的合作博弈和联盟为模糊集的无限模糊联盟区间值合作博弈.首先,利用区间值距离公式定义个人超出值;然后,建立最小化所有局中人个人超出值的最优化模型,进一步得到两类区间值合作博弈的显式解析解,并证明该解的性质;最后,通过数值实例验证所提出区间值合作博弈求解模型的实用性与有效性,为区间值合作博弈提供一种新的求解思路.     

具有交流结构的区间模糊联盟合作对策

当前具有模糊联盟的合作对策研究主要基于任意局中人可自由结盟的基本假设,但现实结盟活动中,局中人普遍受到资源或地位等因素的限制,其合作往往具有交流结构限制。因此,基于Choquet模糊延拓研究了具有交流结构的区间模糊多人合作对策,给出了相应区间模糊联盟平均树解,并通过公理化体系对此解进行了研究。通过供应链纵向合作创新收益分配实例应用,并与区间模糊联盟合作对策的Shapley值进行比较,说明该方法的现实有效性。     

基于广义解的网络合作博弈收益分配模型

网络合作博弈主要研究如何将联盟收益分配给网络合作联盟的每个参与者.考虑到现实生活中很多联盟倾向于保留一部分合作收益用于再发展的情况,对网络合作博弈模型进行扩展,定义广义分配、广义核心和广义谈判集等解的概念,并证明当满足超可加性时,网络合作博弈的广义核心与其广义谈判集存在等价性质.因广义谈判集非空,进而刻画了网络合作博弈广义核心的非空性.算例分析结果表明了广义分配方案的存在性及合理性.     

基于RBS 的合作通信网络公平合作策略

针对合作通信网络中基于纳什议价解(NBS)的合作策略存在用户效用分配不公平的问题,同时考虑用户的最大与最小效用,提出了基于Raiffa-Kalai-Smorodinsk议价解(RBS)的合作策略,并建立了用户合作的条件.仿真结果表明,基于RBS的合作策略在保证网络总效用不变的前提下,具有更好的公平性.     

基于合作博弈的虚拟化资源效用分配策略

效用分配是网格虚拟化资源提供者结成联盟完成用户任务时的关键问题。针对资源提供者建立联盟来提高网格整体效用的情况,研究了利用合作博弈论分配网格资源。给出了资源建立联盟的依据,并以基于费用最小化的MIN_COST算法得到了资源的最优化映射方案。在效用分配中,分别从联盟效用的平均分配和Shapley值分配两方面进行了分析,提出了基于Shapley值的资源联盟效用分配策略。算例结果表明,网格资源联盟可以提高任务的执行效率和资源整体收益,而Shapley值法在均衡联盟个体的效用分配方面也是有效可行的。     

主子阵约束下矩阵方程AX=B的对称最小二乘解

本文主要讨论主子阵约束下矩阵方程AX=B的对称最小二乘解．基于投影定理,巧妙的把最小二乘问题转化为等式问题求解,并利用奇异值分解的方法,给出了该对称最小二乘解的一般表达式．此外,文章还考虑了此对称最小二乘解集合对任一给定矩阵的最佳逼近问题,得到了最佳逼近解,并给出了相应的算法步骤和数值例子．     

Soft cooperation systems and games

A cooperative game for a set of agents establishes a fair allocation of the profit obtained for their cooperation. In order to obtain this allocation, a characteristic function is known. It establishes the profit of each coalition of agents if this coalition decides to act alone. Originally players are considered symmetric and then the allocation only depends on the characteristic function; this paper is about cooperative games with an asymmetric set of agents. We introduced cooperative games with a soft set of agents which explains those parameters determining the asymmetry among them in the cooperation. Now the characteristic function is defined not over the coalitions but over the soft coalitions, namely the profit depends not only on the formed coalition but also on the attributes considered for the players in the coalition. The best known of the allocation rules for cooperative games is the Shapley value. We propose a Shapley kind solution for soft games.     

The Shapley value of cooperative games under fuzzy settings: a survey

We survey the recent developments in the studies of cooperative games under fuzzy environment. The basic problems of a cooperative game in both crisp and fuzzy contexts are to find how the coalitions form vis-á-vis how the coalitions distribute the worth. One of the fuzzification processes assumes that the coalitions thus formed are fuzzy in nature having only partial participations of the players. A second group of researchers fuzzify the worths of the coalitions while a few others assume that both the coalitions and the worths are fuzzy quantities. Among the various solution concepts of a cooperative game, the Shapley value is the most popular one-point solution concept which is characterized by a set of rational axioms. We confine our study to the developments of the Shapley value in fuzzy setting and try to highlight the respective characterizations.     

基于结构元理论的模糊联盟合作对策

仅考虑局中人参与率模糊的合作对策,称为模糊联盟合作对策。将该模型中的模糊参与率用模糊结构元表示,得到基于结构元理论的具有模糊数Choquet积分表达形式的支付函数和Shapley值的理论框架,继而定义结构元线性生成的模糊支付函数和Shapley值表达式。通过算例与区间数的方法进行对比,结果表明：基于结构元理论的模糊联盟合作对策,模型中的模糊数均由结构元线性生成,模糊数之间的四则运算转化成简单的函数表达式之间的四则运算,避免了模糊数之间运算的遍历性,运算简便。运算结果包括区间及区间上各点的隶属度,结果更加精确。     

Cooperative games with multiple attributes

ABSTRACT

In this paper, we introduce the notion of a cooperative game with multiple attributes where players can provide partial participations in multiple attributes and form coalitions. The power or influence of the players due to their multiple attributes is evaluated based on their memberships in the coalitions. Our game therefore, extends the notion of cooperative games with fuzzy coalitions. The Shapley function for this class of games is proposed as a rational and fair solution concept. Every fuzzy game stems out of a specific crisp game under the assumption that the players provide partial memberships in forming multiple coalitions simultaneously. We adopt similar techniques to obtain the cooperative games with multiple attributes from their crisp counterparts and subsequently determine their Shapley functions.     

Role of cooperation in coupling game theory

A coupling game is a new model for partly cooperative and partly non-cooperative games. This paper describes benefits that result when coupling rational cooperation, under some situations, is increased. We prove that if a coupling game is strictly rational and partly cooperative, the higher the coupling factors, the larger the social payoff, which is the sum of the payoffs of all players. Other properties of cooperation in coupling game theory and possible applications are discussed.     

Generalized kings and single-elimination winners in random tournaments

Autonomous Agents and Multi-Agent Systems - For cooperative games with externalities, the problem of optimally partitioning a set of players into disjoint exhaustive coalitions is called coalition...     

On the complexity of core,kernel, and bargaining set

Coalitional games model scenarios where players can collaborate by forming coalitions in order to obtain higher worths than by acting in isolation. A fundamental issue of coalitional games is to single out the most desirable outcomes in terms of worth distributions, usually called solution concepts. Since decisions taken by realistic players cannot involve unbounded resources, recent computer science literature advocated the importance of assessing the complexity of computing with solution concepts. In this context, the paper provides a complete picture of the complexity issues arising with three prominent solution concepts for coalitional games with transferable utility, namely, the core, the kernel, and the bargaining set, whenever the game worth-function is represented in some reasonably compact form. The starting points of the investigation are the settings of graph games and of marginal contribution nets, where the worth of any coalition can be computed in polynomial time in the size of the game encoding and for which various open questions were stated in the literature. The paper answers these questions and, in addition, provides new insights on succinctly specified games, by characterizing the computational complexity of the core, the kernel, and the bargaining set in relevant generalizations and specializations of the two settings. Concerning the generalizations, the paper shows that dealing with arbitrary polynomial-time computable worth functions—no matter of the specific game encoding being considered—does not provide any additional source of complexity compared to graph games and marginal contribution nets. Instead, only for the core, a slight increase in complexity is exhibited for classes of games whose worth functions encode NP-hard optimization problems, as in the case of certain combinatorial games. As for specializations, the paper illustrates various tractability results on classes of bounded treewidth graph games and marginal contribution networks.     

Extremal Pure Strategies and Monotonicity in Repeated Games

The recent development of computational methods in repeated games has made it possible to study the properties of subgame-perfect equilibria in more detail. This paper shows that the lowest equilibrium payoffs may increase in pure strategies when the players become more patient and this may cause the set of equilibrium paths to be non-monotonic. A numerical example is constructed such that a path is no longer equilibrium when the players’ discount factors increase. This property can be more easily seen when the players have different time preferences, since in these games the punishment strategies may rely on the differences between the players’ discount factors. A sufficient condition for the monotonicity of equilibrium paths is that the lowest equilibrium payoffs do not increase, i.e., the punishments should not become milder.     

Cooperative and Competitive Multi-Agent Systems: From Optimization to Games

Multi-agent systems can solve scientific issues related to complex systems that are difficult or impossible for a single agent to solve through mutual collaboration and cooperation optimization. In a multi-agent system, agents with a certain degree of autonomy generate complex interactions due to the correlation and coordination, which is manifested as cooperative/competitive behavior. This survey focuses on multi-agent cooperative optimization and cooperative/non-cooperative games. Starting from cooperative optimization, the studies on distributed optimization and federated optimization are summarized. The survey mainly focuses on distributed online optimization and its application in privacy protection, and overviews federated optimization from the perspective of privacy protection me- chanisms. Then, cooperative games and non-cooperative games are introduced to expand the cooperative optimization problems from two aspects of minimizing global costs and minimizing individual costs, respectively. Multi-agent cooperative and non-cooperative behaviors are modeled by games from both static and dynamic aspects, according to whether each player can make decisions based on the information of other players. Finally, future directions for cooperative optimization, cooperative/non-cooperative games, and their applications are discussed.