不完备偏好下广义强Berge均衡的存在性

本文基于不完备偏好集中元素对应的等价类集是一个偏序集,把不完备偏好问题转化为偏序问题,得到了不完备偏好下的不动点定理,提供一种新的方法证明局中人的决策偏好不满足完备性时,n人非合作博弈中广义强Berge均衡的存在性.     

离散空间中的一般均衡理论

在消费者偏好函数是强凸、连续和严格单调的条件下给出了不可分市场的一般均衡存在定理,因而也给出了离散空间中一般均衡存在的一个充分条件.     

基于显示、生成偏好的序贯模糊选择函数的研究

本文分别在普通情况以及模糊情况下,对显示偏好、生成偏好合理化的序贯选择函数进行了一定的研究。首先,研究了该序贯合理的选择函数的选择结果与选择顺序无关的条件,其次,研究了选择函数与该序贯合理的选择函数之间的关系。     

不确定偏好序下的双边匹配博弈

针对带有不确定偏好序的双边匹配问题,现有方法大都仅注重整体收益之和,忽略了参与人的个体收益以及在交互选择中的策略运用.基于最大满意度准则,给出不确定序下的收益（满意度）矩阵的推导过程;然后,从个体理性视角,结合矩阵博弈的思想构建一种兼顾整体和个体收益的博弈匹配优化模型,并证明模型最优解满足纳什均衡.最后,进一步探讨各种策略选择及其优劣分析.     

约束形式下广义最大元Nash均衡的存在性

运用广义最大元方法在非传递性偏好下给出了博弈均衡的存在性定理,推广了一些经典的博弈均衡存在性定理.在文中介绍策略式博弈的Nash均衡具有宽泛的条件,在微观经济理论中有广泛的应用.     

医疗服务市场质量竞争博弈模型

以社会福利最大化为目标,建立双寡头垄断下医疗机构质量价格序贯博弈模型,以及在医疗服务价格和财政补偿双重规制下的政府和医疗机构之间的两阶段博弈模型.研究发现:由于医疗服务市场价格竞争削弱了质量竞争效应,序贯博弈的纳什均衡质量低于以社会福利最大化为目标的社会均衡质量.当医疗机构的固定成本控制在某个范围时,政府双重规制下的均衡质量优于医疗机构质量价格序贯博弈下的均衡质量,从而从理论上证明了政府双重规制的有效性.     

均衡度公理化定义的改进

研究均衡度概念的公理化定义及其构造问题.首先,借助实例说明现有均衡度定义存在的问题;随后,在分析均衡度概念的特点和典型均衡度函数的图形的基础上,给出一种新的均衡度公理化定义.接着,讨论均衡度函数的构造问题,给出四类常用的均衡度函数,证明了均衡度函数与一类单调函数的复合仍是均衡度.最后,讨论了新的均衡度定义与原定义之间的关系以及四类常见均衡度函数之间的关系.     

经营成本不对称企业研发合作的期权博弈模型

本文研究了经营成本不对称企业的研发合作投资策略，给出企业作为追随者、领先者和同时投资者的投资临界值和收益，并分析了可能形成的均衡及其形成条件。当经营成本优势明显时，企业进行序贯投资；当先动优势明显时，低成本企业抢先投资；其他情况下，企业同时投资。     

供应链竞争下产品族定制规划博弈模型及分析

在大规模定制下,产品族定制规划不仅需确定各定制产品的性能定位、还需面对市场价格博弈.考虑制造商对市场的依存、及市场对高质量产品的偏好,分别构建了定制规划的一维和多维扩展Hotelling模型,基于模型的推理、计算与分析,首先证明了在一维产品族定制规划下各制造商可实现价格均衡和性能定位均衡;同时,证实质量因素能驱动均衡性能定位向高端转移,并通过价格博弈、促使制造商定制生产更高质量的产品,故从质量角度诠释了市场不断向高端进化的内部机理;其次,证实了多维产品族定制规划博弈仅存在均衡价格数值解、无全局精确解;最后,基于均衡价格数值解的聚类分析,提出博弈结构均衡概念,证实在多维定制规划中存在博弈结构均衡、并以此有效诠释了价格竞争中"价格维持-价格变更"这一价格循环波动现象的内在运作机理.博弈分析及结论将为企业评估、选择恰当的产品族定制规划策略提供有效决策支持.     

拓扑向量空间中带上下界均衡问题解的存在性

主要研究了拓扑空间上的带上下界均衡问题和带限制条件的上下界均衡问题解的存在性.在非凸集上借助转移紧闭值等有关概念研究其相应均衡问题解的存在性,与一些作者的研究思路较为不同,得到了相应均衡问题解的存在条件,推广了一些作者在凸集上研究的相应结果,并且为相应均衡问题研究提供了一个新的视角.     

Sequential Stackelberg equilibria in two-person games

The concept of sequential Stackelberg equilibrium is introduced in the general framework of dynamic, two-person games defined in the Denardo contracting operator formalism. A relationship between this solution concept and the sequential Nash equilibrium for an associated extended game is established. This correspondence result, which can be related to previous results obtained by Baar and Haurie (1984), is then used for studying the existence of such solutions in a class of sequential games. For the zero-sum case, the sequential Stackelberg equilibrium corresponds to a sequential maxmin equilibrium. An algorithm is proposed for the computation of this particular case of equilibrium.This research was supported by SSHRC Grant No. 410-83-1012, NSERC Grant No. A4952, and FCAR Grants Nos. 86-CE-130 and EQ-0428.The authors thank T. R. Bielecki and J. A. Filar, who pointed out some mistakes and helped improving the paper.At the time of this research, this author was with GERMA, Ecole Mohammedia d'Ingénieurs, Rabat, Morocco.     

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.     

Nondominated equilibrium solutions of a multiobjective two-person nonzero-sum game in extensive form and corresponding mathematical programming problem

In most of studies on multiobjective noncooperative games, games are represented in normal form and a solution concept of Pareto equilibrium solutions which is an extension of Nash equilibrium solutions has been focused on. However, for analyzing economic situations and modeling real world applications, we often see cases where the extensive form representation of games is more appropriate than the normal form representation. In this paper, in a multiobjective two-person nonzero-sum game in extensive form, we employ the sequence form of strategy representation to define a nondominated equilibrium solution which is an extension of a Pareto equilibrium solution, and provide a necessary and sufficient condition that a pair of realization plans, which are strategies of players in sequence form, is a nondominated equilibrium solution. Using the necessary and sufficient condition, we formulate a mathematical programming problem yielding nondominated equilibrium solutions. Finally, giving a numerical example, we demonstrate that nondominated equilibrium solutions can be obtained by solving the formulated mathematical programming problem.     

Redefinition of Belief Distorted Nash Equilibria for the Environment of Dynamic Games with Probabilistic Beliefs

In this paper, a new concept of equilibrium in dynamic games with incomplete or distorted information is introduced. In the games considered, players have incomplete information about crucial aspects of the game and formulate beliefs about the probabilities of various future scenarios. The concept of belief distorted Nash equilibrium combines optimization based on given beliefs and self-verification of those beliefs. Existence and equivalence theorems are proven, and this concept is compared to existing ones. Theoretical results are illustrated using several examples: extracting a common renewable resource, a large minority game, and a repeated Prisoner’s Dilemma.     

Selection of a correlated equilibrium in Markov stopping games

This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players’ decisions according to some optimality criterion. This is a form of equilibrium selection. Examples of correlated equilibria in nonzero-sum games related to the best choice problem are given. Several concepts of criteria for selecting a correlated equilibrium are used.     

不确定性下强Berge均衡的存在性

在已知不确定参数变化的范围下,研究了非合作博弈与广义非合作博弈的强Berge均衡的存在性,基于强Berge均衡与不确定性下非合作博弈的强Nash均衡的概念,给出了不确定参数下非合作博弈与广义非合作博弈的强Berge均衡的定义,并利用Fan-Glicksberg不动点定理证明其存在性,最后用算例验证其可行性.     

多重均衡选择中的风险占优与混合策略

均衡选择理论是博弈理论的重要组成部分.风险占优均衡是人们经济决策或行为的一个主要结果.利用混合策略及其性质和“抵制”的概念,“支持”了海萨尼和泽尔腾用公理定义的风险占优概念,且具体给出了识别风险占优均衡的标准和方法,并把它们推广到对称博弈中去.最后对均衡占优的直觉概念和风险占优相冲突的一些博弈进行了类似的讨论.     

Some remarks on the folk theorem in game theory

It is argued that although the pathological multiplicity of Nash equilibria of super games stated by the folk theorem can be removed by introducing limited observations into super games with a continuum of players, the consideration of super games in terms of the Nash equilibrium concept involves a more fundamental and conceptual difficulty.     

Cooperative games with imcomplete information

A bargaining solution concept which generalizes the Nash bargaining solution and the Shapley NTU value is defined for cooperative games with incomplete information. These bargaining solutions are efficient and equitable when interpersonal comparisons are made in terms of certainvirtual utility scales. A player's virtual utility differs from his real utility by exaggerating the difference from the preferences of false types that jeopardize his true type. In any incentive-efficient mechanism, the players always maximize their total virtual utility ex post. Conditionally-transferable virtual utility is the strongest possible transferability assumption for games with incomplete information.