具有区间联盟值n人对策的Shapley值

本文提出了一类具有区间联盟收益值n人对策的Shapley值.利用区间数运算有关理论,通过建立公理化体系,对具有区间联盟收益值n人对策的Shapley值进行深入研究,证明了这类n人对策Shapley值存在性与唯一性,并给出了此Shapley值的具体表达式及一些性质.最后通过一个算例检验了其有效性与正确性.     

具有判断值支付的合作对策的M-S值

针对联盟支付以判断值给出的n人合作对策问题,提出了一个基于1-9 判断标度的合作对策Multiplicative-Shapley 值求解公式. 首先给出了判断值平均支付函数的定义,研究了判断值的一致性及其调整方法. 其次通过定义相应的特征函数,给出了具有判断值支付的n人合作对策的优超、伪凸、伪核心、单位元等系列概念,并由此提出一个满足3条公理的Multiplicative-Shapley 值公式. 最后通过一个算例,验证了Multiplicative-Shapley 值公式的可行性和有效性.     

n阶线性模糊微分方程的结构元解法

研究了n阶线性模糊微分方程的模糊初值问题,将n阶线性模糊微分方程转化成一阶线性模糊微分方程组,利用结构元方法将模糊线性微分方程组转化成两个分明的线性微分方程组,通过分明的线性微分方程组的解构造出原n阶线性模糊微分方程的解.最后,给出了具体的算例.     

优先联盟间有权限结构限制的合作对策的联盟限制Owen值

考虑局中人结成优先联盟参与合作,并且优先联盟之间具有权限结构限制的合作对策,利用Owen值的两阶段分配思路并考虑到优先联盟之间权限结构对合作的限制,定义这类合作对策一个解,证明了解的公理化结论,并验证了公理化条件的独立性.最后给出了算例分析,说明解在合作收益分配问题的应用.     

一类具有限制联盟结构的合作对策的两阶段Shapley值

讨论一类具有限制联盟结构的合作对策,其中局中人通过优先联盟整体参与大联盟的合作,同时优先联盟内部有合取权限结构限制,利用两阶段Shapley值的分配思想并考虑到权限结构对优先联盟内合作的限制,给出了此类合作对策的解。 该解可看做具有联盟结构的合作对策的两阶段Shapley值的推广。 证明了该解满足的公理化条件,并验证了这些条件的独立性。     

基于多维线性扩展的模糊联盟合作对策tau值性质与计算方法

研究模糊联盟合作对策tau值的计算方法及其性质. 利用多维线性扩展方法定义了模糊联盟合作对策的tau值, 证明了其存在性、唯一性等性质, 并推导出基于多维线性扩展凸模糊联盟合作对策tau值的计算公式. 研究结果发现, 基于多维线性扩展的模糊联盟合作对策tau值是对清晰联盟合作对策tau值的扩展, 而清晰联盟合作对策tau值仅是其特例. 特别地, 对于凸模糊联盟合作对策, 利用其tau值计算公式, 可进一步简化求解过程.     

模糊联盟合作对策的平均树解

给出图对策中平均树解的拓展形式, 证明其是满足分支有效性和分支公平性的唯一解. 针对具有模糊联盟的图对策, 提出了一种模糊分配, 即模糊平均树解. 当模糊联盟图对策为完全图对策时, 模糊平均树解等于模糊Shapley值. 最后, 讨论了模糊平均树解与模糊联盟核心之间的关系, 并进行了实例论证.     

n人合作博弈中k人稳定联盟的存在性

本文在以Nash谈判解为分配准则的前提下,考虑—个n人合作博弈中核心不为空的k人稳定合作联盟的存在性.首先,考察了2人联盟的情形,给出稳定2人联盟的概念并进一步证明在n人合作博弈中必然存在一个稳定2人联盟.接着分析稳定k人联盟,并给出一个稳定k人联盟存在的充分条件.进一步地,设计了一个算法,寻找与存在稳定k人联盟等价的一个匹配.另外,本文还给出了—个K人联盟中所有局中人获得的收益高于其内部子联盟的充分条件.最后给出一个算例,验证本文理论和方法的可行性.     

多目标线性生产规划的模糊联盟对策

研究多目标生产规划的模糊联盟对策的求解问题,提出了求解多目标模糊联盟对策的Shapley值方法.通过建立多目标线性生产规划的模糊联盟对策模型,提出了多目标对策转化为多个单目标对策的权重分析法.结合多目标线性生产规划问题的实例,给出不同权重系数下局中人合作的利益分配策略.     

模糊联盟合作对策的收益分配研究

针对现实环境中联盟组成的不确定性, 本文研究了具有模糊联盟的合作对策求解问题。提出了模糊联盟合作对策的一种新的分配方式,即平均分摊解,并给出了这种解与模糊联盟合作对策Shapley值一致的充分条件。同时,还提出了模糊联盟合作对策的Shapley值的一个重要性质。最后,结合算例进行了分析论证。     

The consistent Shapley value for hyperplane games

A new value is defined for n-person hyperplane games, i.e., non-sidepayment cooperative games, such that for each coalition, the Pareto optimal set is linear. This is a generalization of the Shapley value for side-payment games. It is shown that this value is consistent in the sense that the payoff in a given game is related to payoffs in reduced games (obtained by excluding some players) in such a way that corrections demanded by coalitions of a fixed size are cancelled out. Moreover, this is the only consistent value which satisfies Pareto optimality (for the grand coalition), symmetry and covariancy with respect to utility changes of scales. It can be reached by players who start from an arbitrary Pareto optimal payoff vector and make successive adjustments.     

The collective value: a new solution for games with coalition structures

In this study, we provide a new solution for cooperative games with coalition structures. The collective value of a player is defined as the sum of the equal division of the pure surplus obtained by his coalition from the coalitional bargaining and of his Shapley value for the internal coalition. The weighted Shapley value applied to a game played by coalitions with coalition-size weights is assigned to each coalition, reflecting the size asymmetries among coalitions. We show that the collective value matches exogenous interpretations of coalition structures and provide an axiomatic foundation of this value. A noncooperative mechanism that implements the collective value is also presented.     

Cooperation in dividing the cake

This paper defines models of cooperation among players partitioning a completely divisible good (such as a cake or a piece of land). The novelty of our approach lies in the players’ ability to form coalitions before the actual division of the good with the aim to maximize the average utility of the coalition. A social welfare function which takes into account coalitions drives the division. In addition, we derive a cooperative game which measures the performance of each coalition. This game is compared with the game in which players start cooperating only after the good has been portioned and has been allocated among the players. We show that a modified version of the game played before the division outperforms the game played after the division.     

Bisection property of the kernel

Maschler, Peleg and Shapley make use of the bisection property of the kernel to provide an interpretation of the kernel for n-person game with grand coalition. We develop the similar results for any n-person game with coalition structure.     

Power,Embedded Games,and Coalition Formation

Applications of game theory frequently presume but do not show that social structures contain games. This study shows that multiple games are embedded in strong power structures and that power is exercised because 1) the game of those low in power contains a dilemma whereas 2) the game of those high in power does not. As in previous analyses, we find those low in power play the Prisoner's Dilemma game. New to this analysis is the discovery that those high in power play the Privileged game, a game with no dilemma. Also new is the extension of the analysis to the design of coalitions. That extension shows that, when coalition formation succeeds, it eliminates the dilemma of those low in power by transforming their game from Prisoner's Dilemma to Privileged. By contrast, exactly the same coalition structure does not alter the game played by those high in power. Applying well-known game theoretic solution concepts, we predict that low power coalitions will countervail power, but that coalitions of those high in power will not affect power exercise. Experiments testing this theory investigate 1) coalitions of those high in power, 2) low power coalitions organized against multiple high power positions, and 3) opposed coalitions struggling for power against each other. Results strongly support the theory.     

The Harsanyi paradox and the “right to talk” in bargaining among coalitions

We describe a coalitional value from a non-cooperative point of view, assuming coalitions are formed for the purpose of bargaining. The idea is that all the players have the same chances to make proposals. This means that players maintain their own “right to talk” when joining a coalition. The resulting value coincides with the weighted Shapley value in the game between coalitions, with weights given by the size of the coalitions. Moreover, the Harsanyi paradox (forming a coalition may be disadvantageous) disappears for convex games.     

On the Convenience to Form Coalitions or Partnerships in Simple Games

A partnership in a cooperative game is a coalition that possesses an internal structure and, simultaneously, behaves as an individual member. Forming partnerships leads to a modification of the original game which differs from the quotient game that arises when one or more coalitions are actually formed. In this paper, the Shapley value is used to discuss the convenience to form either coalitions or partnerships. To this end, the difference between the additive Shapley value of the partnership in the partnership game and the Shapley alliance value of the coalition, and also between the corresponding value of the internal and external players, are analysed. Simple games are especially considered. Research partially supported by Grant BFM 2003-01314 of the Science and Technology Spanish Ministry and the European Regional Development Fund.     

Two noncooperative games between a coalition and its surrounding in a class of n-person games with constant sum

A cooperative game engendered by a noncooperative n-person game (the master game) in which any subset of n players may form a coalition playing an antagonistic game against the residual players (the surrounding) that has a (Nash equilibrium) solution, is considered, along with another noncooperative game in which both a coalition and its surrounding try to maximize their gains that also possesses a Nash equilibrium solution. It is shown that if the master game is the one with constant sum, the sets of Nash equilibrium strategies in both above-mentioned noncooperative games (in which a coalition plays with (against) its surrounding) coincide.     

Cooperative games of choosing partners and forming coalitions in the marketplace

Two games of interacting between a coalition of players in a marketplace and the residual players acting there are discussed, along with two approaches to fair imputation of gains of coalitions in cooperative games that are based on the concepts of the Shapley vector and core of a cooperative game. In the first game, which is an antagonistic one, the residual players try to minimize the coalition's gain, whereas in the second game, which is a noncooperative one, they try to maximize their own gain as a coalition. A meaningful interpretation of possible relations between gains and Nash equilibrium strategies in both games considered as those played between a coalition of firms and its surrounding in a particular marketplace in the framework of two classes of n-person games is presented. A particular class of games of choosing partners and forming coalitions in which models of firms operating in the marketplace are those with linear constraints and utility functions being sums of linear and bilinear functions of two corresponding vector arguments is analyzed, and a set of maximin problems on polyhedral sets of connected strategies which the problem of choosing a coalition for a particular firm is reducible to are formulated based on the firm models of the considered kind.