基于三角模糊数的凸合成模糊对策解的结构

将凸合成模糊对策的特征函数用三角模糊数的形式表示出来,并以三角模糊数表示局中人的参与度,从而建立了一个新的凸合成模糊合作对策的模型.在此模型的基础上,给出了凸合成模糊对策的三角核心和三角稳定集,并证明了上述解可由子对策的核心和稳定集表达出来.     

凸随机合作对策的核心

本文将凸性扩展到随机合作对策中,从而得到凸随机合作对策具有超可加性与非空的核心,且凸随机合作对策的核心满足Minkowski和与Minkowski差.     

基于Selectope解集和局中人最大满意度的合作对策解的研究

针对决策者在获取Selectope解集后难以聚焦到最终分配方案上的问题,论文对合作对策的解集进行了研究。首先借助Harsanyi红利在局中人中进行分配的思想,得到Selectope解集作为研究问题的可行域。之后,在局中人完全理性的条件下,充分考虑局中人参与合作的初衷,运用超出值的概念,构建了描述局中人最大满意度的目标函数,进而得到基于Selectope解集与局中人最大满意度的非线性规划模型,用于合作对策收益分配问题的求解。最后,通过算例验证了该求解思路的可行性与求解结果的合理性。研究结果表明,论文提出的求解思路能够有效缩减Selectope解集的体量,为决策者提供一个精炼的抉择空间,在一定程度上拓展了Selectope解集的应用,同时,构建的局中人最大满意度的非线性函数对局中人满意度研究也有一定的参考价值。     

弱1—凸对策及其解的性质

本文提出了一类特殊的ｎ人合作对策模型─—弱１—凸对策，研究了弱１—凸对策的解的性质，并证明弱１—凸对策的解满足所有常见的公理化特征．     

支付函数为模糊数的多目标多人合作对策的纳什谈判解

讨论了多目标多人合作对策中支付函数是模糊数的情形,利用模糊数学相关理论, 对Nash提出的6条公理进行拓广,并证明这种情况下λ-纳什谈判解的存在性.     

最大收益支撑森林对策

本文在无向图上定义了最大收益支撑森林对策.首先研究了核心的非空性和表示性,给出了核心的弱化定义;其次给出了核心中分配属于核的充要条件,并利用迭代步骤证明了核仁即为核心和核的交集;最后给出了含割点图中核仁的分解定理.     

直觉模糊支付合作对策的核仁解

本文主要研究支付值为直觉模糊集的合作对策问题及其模糊核仁解.首先定义了直觉模糊集的得分函数和精确函数,并给出其排序方法,得到基于直觉模糊集的合作对策模型和适合这种模型的相应定义,同时提出了直觉模糊核仁解的概念;其次运用新的排序方法将求核仁解的问题转化为求解双目标非线性规划问题;最后通过实例分析验证了该方法的可行性和有效性。     

三元区间支付合作对策的核心解

基于三元区间数,提出三元区间支付合作对策理论,利用三元区间数的运算及序关系,建立了三元区间支付合作对策模型和具有偏好标准的三元区间支付合作对策模型,研究相应模型的几类核心解,如区间核心、区间优超核心及q-区间核心等,讨论了各相关核心解之间的关系,并加以证明.最后通过实例分析,验证了三元区间支付合作对策理论,具有一定的参考价值与现实意义,是对模糊支付合作对策理论的不断完善.     

拟不变凸集值优化问题严有效解的最优性条件

在赋范线性空间中借助切导数研究集值优化问题的严有效性．当目标函数和约束函数相对于同一向量函数为拟不变凸时,利用凸集分离定理给出了集值优化问题取得严有效元的Kuhn—Xhcker型最优陛必要条件．利用切导数的性质,用构造性方法得到了拟不变凸集值优化问题取得严有效元的充分条件．     

可转移效用下的动态模糊联盟的广义核心解

利用模糊数学相关理论,对具有可转移效用的模糊合作对策进行了研究.采用调整相应系数的方法给出了此类对策的广义核心解和广义稳定集的概念,讨论了它们之间的关系.提出一种新的分配方案—不将联盟总收益分配给所有局中人,而保留一部分从而实现收益的再分配.该成果解决了对策传统解在现实应用中的局限性,特别是对现实生活中的资源再分配问题具有一定的参考和应用价值.     

Bargaining sets and the core in partitioning games

Partitioning games are useful on two counts: first, in modeling situations with restricted cooperative possibilities between the agents; second, as a general framework for many unrestricted cooperative games generated by combinatorial optimization problems.We show that the family of partitioning games defined on a fixed basic collection is closed under the strategic equivalence of games, and also for taking the monotonic cover of games. Based on these properties we establish the coincidence of the Mas-Colell, the classical, the semireactive, and the reactive bargaining setswith the core for interesting balanced subclasses of partitioning games, including assignment games, tree-restricted superadditive games, and simple network games. Prepared during the author’s Bolyai János Research Fellowship. Also supported by OTKA grant T46194.     

A short proof of convexity of step-out–step-in sequencing games

The Step out–Step in sequencing game is a particular example of a game from the sequencing game framework of Curiel, Perderzoli, and Tijs, where coalitions of players in a queue may reorder themselves to improve the their overall cost, under some restrictions. Musegaas, Borm and Quant proved, in two papers, that a simple greedy algorithm correctly computes the valuation of a coalition, and that the game is convex. These proofs entail rather involved case analyses; in this note, we give short proofs of both results.     

Limit Consistent Solutions in Noncooperative Games

Strong and limit consistency in finite noncooperative games are studied. A solution is called strongly consistent if it is both consistent and conversely consistent (Ref. 1). We provide sufficient conditions on one-person behavior such that a strongly consistent solution is nonempty. We introduce limit consistency for normal form games and extensive form games. Roughly, this means that the solution can be approximated by strongly consistent solutions. We then show that the perfect and proper equilibrium correspondences in normal form games, as well as the weakly perfect and sequential equilibrium correspondences for extensive form games, are limit consistent.     

The not-quite non-atomic game: Non-emptiness of the core in large production games

We show that, in cooperative production games, when the production functions are not concave, the core may well be empty. However, as the number of players increases (subject to some regularity conditions), the relative deficit obtained by using concavified functions decreases to zero. Furthermore, differentiability of the functions will cause the absolute deficit to go to zero.     

A natural selection from the core of a TU game: the core-center

We present a new allocation rule for the class of games with a nonempty core: the core-center. This allocation rule selects a centrally located point within the core of any such game. We provide a deep discussion of its main properties.     

The Compromise Value for Cooperative Games with Random Payoffs

This paper introduces and studies the compromise value for cooperative games with random payoffs, that is, for cooperative games where the payoff to a coalition of players is a random variable. This value is a compromise between utopia payoffs and minimal rights and its definition is based on the compromise value for NTU games and the τ-value for TU games. It is shown that the nonempty core of a cooperative game with random payoffs is bounded by the utopia payoffs and the minimal rights. Consequently, for such games the compromise value exists. Further, we show that the compromise value of a cooperative game with random payoffs coincides with the τ-value of a related TU game if the players have a certain type of preferences. Finally, the compromise value and the marginal value, which is defined as the average of the marginal vectors, coincide on the class of two-person games. This results in a characterization of the compromise value for two-person games.I thank Peter Borm, Ruud Hendrickx and two anonymous referees for their valuable comments.     

Core Solutions in Vector-Valued Games

In this paper, we analyze core solution concepts for vector-valued cooperative games. In these games, the worth of a coalition is given by a vector rather than by a scalar. Thus, the classical concepts in cooperative game theory have to be revisited and redefined; the important principles of individual and collective rationality must be accommodated; moreover, the sense given to the domination relationship gives rise to two different theories. Although different, we show the areas which they share. This analysis permits us to propose a common solution concept that is analogous to the core for scalar cooperative games.     

Convex games with an infinite number of players and sequencing situations

In this paper we study convex games with an infinite countable set of agents and provide characterizations of this class of games. To do so, and in order to overcome some shortcomings related to the difficulty of dealing with infinite orderings, we need to use a continuity property. Infinite sequencing situations where the number of jobs is infinite countable can be related to convex cooperative TU games. It is shown that some allocations turn out to be extreme points of the core of an infinite sequencing game.     

An acyclic relation for comparison of bargaining powers of coalitions and its interrelationship with bargaining set

This paper proposes a method to compare bargaining power of coalitions within the framework of games in coalition form with transferable utility. The method is expressed by a relation on the set of all coalitions in a game, the relation which is defined based on the players’ bargaining power. It is shown in this paper that the newly defined relation satisfies acyclicity. Also, it is verified in this paper that the set of all individually rational payoff configurations under which all coalitions have the equal bargaining power coincides with the bargaining set. Some examples demonstrate how the newly proposed method works.