一般交叉规划与经济均衡模型

本文首先给出了有多个子规划的一般交叉规划模型,然后把它转化为抽象经济模型,并给出其均衡解存在的条件.最后利用一般交叉规划建立了一类非合作型寡头垄断市场的均衡模型.     

多目标大博弈中弱Pareto-Berge均衡的存在性

研究了具有任意多个局中人的非合作多目标博弈(多目标大博弈).基于一般非合作博弈中的Berge均衡概念,定义多目标大博弈中的弱Pareto-Berge均衡.进一步推广了截口定理,得到新的截口定理,并且利用这个新的截口定理证明多目标大博弈中弱Pareto-Berge均衡的存在性.多目标大博弈中弱Pareto-Nash均衡的存在性结论可作为弱Pareto-Berge均衡存在性的特例给出.     

一种n人静态博弈纯策略纳什均衡存在性判别法

本首先给出了n人静态博弈纯策略纳什均衡存在的充要条件。然后给出n人静态博弈纯策略纳什均衡存在性的一种判别方法。最后在判别纯策略纳什均衡存在的条件下，给出判定该静态博弈存在多少纯策略纳什均衡以及哪些纯策略组合是纯策略纳什均衡(解)的方法。     

Brouwer定理与均衡价格

本文详细论述了在一般均衡体系中均衡价格存在性定理与Brouwer不动点定理是等价的。即，均衡价格π ζ（π）≤0就是Brouwer定理中的不动点x^∧ f(x^∧)=x^∧并给出证明。这一等价性为计算均衡价格提供了坚实的理论依据，从而肯定了利用Brouwer定理寻找不动点的方法计算均衡价格的计算方法是可靠的。因此具有特别重要的实用意义。     

一类具有非空核的拟均衡对策

自 Scarf 给出 n 人没有边支付对策的核存在的条件后,很多人致力于研究一般的没有边支付对策的核.但情况比较复杂,一般的没有边支付对策核非空要求的条件较强,即使是均衡对策,也不能保证核的非空性.因而,Weber 引进了拟均衡对策.本文研究了一类拟均衡对策,它们具有非空的核.本文中的定理1改进了文献[2]中的主要结论.     

双人静态博弈纯战略纳什均衡存在性判别

本文给出了双人有限静态博弈纯战略纳什均衡存在性的一种判别方法。并且，在纳什均衡存在的条件下，本判别法将给出纳什均衡解及解的唯一性判别。     

全支付拍卖模型的信息结构及其对均衡的影响分析——纪念李国平院士吴新谋教授诞辰100周年

研究全支付拍卖模型中参与人的参与结构以及均衡问题.首先给出了非对称信息下参与人的参与选择问题,分析了异质参与人的参与选择. 尔后给出了参与人参与均衡策略,给出当参与人估价分布函数在对称和非对称情形时, 竞赛中的对称均衡策略.最后给出了当均衡存在时, 竞争对手对均衡分布函数的估计.     

全支付拍卖模型的信息结构及其对均衡的影响分析

研究全支付拍卖模型中参与人的参与结构以及均衡问题.首先给出了非对称信息下参与人的参与选择问题,分析了异质参与人的参与选择.尔后给出了参与人参与均衡策略,给出当参与人估价分布函数在对称和非对称情形时,竞赛中的对称均衡策略.最后给出了当均衡存在时,竞争对手对均衡分布函数的估计.     

基于RBC模型的动态随机一般均衡的数值解

以一般均衡为框架,引入随机变量的动态随机一般均衡系统,由于模型的庞大和函数形式的复杂,往往不能给出明确的数值解.本文给出几种操作性强的、有效的寻求一般化模型数值解的方法,并通过介绍模型参数确定的办法,使得理论的模型有了现实的含义.     

连续区间策略下二人零和对策问题研究

考虑连续区间策略下的二人零和对策问题,研究其均衡策略的存在性。首先分析了完全信息下的二人零和对策问题,证明了该问题均衡策略的存在性并给出求解方法。然后进一步研究了收益函数不确定的不完全信息二人零和对策问题,在各局中人都认为对方是风险厌恶型的假设下,分析该类对策纯策略均衡的存在性,并通过研究纯策略均衡存在的充要条件给出判断并寻找纯策略均衡解的方法。最后给出一个数值算例,验证本文所提出方法的可行性。     

Mathematical analysis of an eco-epidemiological predator–prey model with stage-structure and latency

In this paper, an eco-epidemiological predator–prey model with stage structure for the prey and a time delay describing the latent period of the disease is investigated. By analyzing corresponding characteristic equations, the local stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the endemic equilibrium is addressed. The existence of Hopf bifurcations at the endemic equilibrium is established. By using Lyapunov functionals and LaSalle’s invariance principle, sufficient conditions are obtained for the global asymptotic stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the endemic equilibrium of the model.     

A network formulation of market equilibrium problems and variational inequalities

This paper shows that market equilibrium problems of production may generally be modelled as equilibrium flow problems in networks and that their equilibrium conditions can be visualized as a variational inequality. This connection would allow us to transplant directly elements of the well-developed theory of equilibrium flow in networks to the theory of market equilibrium.     

一类带有一般接触率和常数输入的流行病模型的全局分析

借助极限系统理论和构造适当的Liapunov函数,对带有一般接触率和常数输入的SIR型和SIRS型传染病模型进行讨论．当无染病者输入时,地方病平衡点存在的阈值被找到A·D2对相应的SIR模型,关于无病平衡点和地方病平衡点的全局渐近稳定性均得到充要条件;对相应的SIRS模型,得到无病平衡点和地方病平衡点全局渐近稳定的充分条件．当有染病者输入时,模型不存在无病平衡点．对相应的SIR模型,地方病平衡点是全局渐近稳定的;对相应的SIRS模型,得到地方病平衡点全局渐近稳定的充分条件．     

基于训练和过滤的期望均衡及其实现路径

期望均衡是博弈局中人或局外人对于博弈均衡点的一致期望,强调互利共赢,它要求博弈群体的每个成员对期望均衡点有一个共同的预期.显然,基于纳什均衡的帕累托优化组合策略是一个比纳什均衡更有效的期望均衡.要实现期望均衡,可采用局中人参与的训练与学习使得群体的预期一致,也可采用第三方过滤器来达到期望目标.在期望均衡的概率分布下,个体行为的偏离不能比均衡态取得更多收益.否则,训练就是无效的,第三方过滤器就是不公平的.     

Global dynamics of a delayed predator–prey model with stage structure for the predator and the prey

A delayed predator–prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each feasible equilibrium of the system is discussed, and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of the persistence theory for infinite dimensional systems, it is proven that the system is permanent if the coexistence equilibrium exists. By using suitable Lyapunov functions and the LaSalle invariant principle, it is shown that the trivial equilibrium is globally stable when both the predator–extinction equilibrium and the coexistence equilibrium do not exist, and that the predator–extinction equilibrium is globally stable when the coexistence equilibrium does not exist. Further, sufficient conditions are obtained for the global stability of the coexistence equilibrium. Numerical simulations are carried out to illustrate the main theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

TIME INCONSISTENCY AND REPUTATION IN MONETARY POLICY: A STRATEGIC MODELLING IN CONTINUOUS TIME

This article develops a model to examine the equilibrium behavior of the time inconsistency problem in a continuous time economy with stochastic and endogenized dis-tortion. First, the authors introduce the notion of sequentially rational equilibrium, and show that the time inconsistency problem may be solved with trigger reputation strategies for stochastic setting. The conditions for the existence of sequentially rational equilibrium are provided. Then, the concept of sequentially rational stochastically stable equilibrium is introduced. The authors compare the relative stability between the cooperative behavior and uncooperative behavior, and show that the cooperative equilibrium in this monetary policy game is a sequentially rational stochastically stable equilibrium and the uncooper-ative equilibrium is sequentially rational stochastically unstable equilibrium. In the long run, the zero inflation monetary policies are inherently more stable than the discretion rules, and once established, they tend to persist for longer periods of the time.     

Fuzzy weighted equilibrium multi-job assignment problem and genetic algorithm

In this paper, the equilibrium optimization problem is proposed and the assignment problem is extended to the equilibrium multi-job assignment problem, equilibrium multi-job quadratic assignment problem and the minimum cost and equilibrium multi-job assignment problem. Furthermore, the mathematical models of the equilibrium multi-job assignment problem and the equilibrium multi-job quadratic assignment problem with fuzzy parameters are formulated. Finally, a genetic algorithm is designed for solving the proposed programming models and some numerical examples are given to verify the efficiency of the designed algorithm.     

Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique

The main goal of this paper is to introduce and study bilevel vector equilibrium problems. We first establish some existence results for solutions of vector equilibrium problems and mixed vector equilibrium problems. We study the existence of solutions of bilevel vector equilibrium problems by considering a vector Thikhonov-type regularization procedure. By using this regularization procedure and existence results for mixed vector equilibrium problems, we establish some existence results for solutions of bilevel vector equilibrium problems. By using the auxiliary principle, we propose an algorithm for finding the approximate solutions of bilevel vector equilibrium problems. The strong convergence of the proposed algorithm is also studied.     

寡头垄断市场三度价格歧视动态博弈分析

对两寡头厂商2元市场用完全信息动态博弈的方法分析了实施三度价格歧视情形和统一定价情形的均衡产量,均衡价格和均衡总收益,并研究了这两种情形三个指标之间的关系.结果显示,在两个子市场的需求函数为线性需求的条件下,统一定价的市场均衡产量等于歧视定价的市场均衡产量;统一定价的均衡价格是歧视定价时两个子市场均衡价格的加权平均;统一定价的市场均衡总收益小于歧视定价的市场均衡总收益.     

Mathematical Programming with System of Equilibrium Constraints

In this paper, we study the mathematical program with system of equilibrium constraints. This problem contains bilevel program with system of equilibrium constraints, semi-infinite program with system of equilibrium constraints, mathematical program with Nash equilibrium constraints, mathematical program with system of mixed variational like inequalities constraints. We establish the existence theorems of mathematical program with system of equilibrium constraints under various assumptions.