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.     

具有随机需求的多种差异产品供应链网络均衡模型研究

针对产品的品牌和产地存在的差异性,研究了供应链网络的均衡模型,构建了具有随机需求的多种差异产品的供应链网络均衡模型.运用随机效用理论和多项式logit模型分析了需求市场上产品的随机选择问题,利用变分不等式的形式给出了制造商、零售商,需求市场以及整个供应链网络的均衡条件,并给出了经济解释.最后,通过算例验证了模型的合理性.     

汽车生产厂家的定价策略博弈模型

讨论了企业在经营管理中的最优化问题,构建了汽车行业在寡头垄断市场中各厂商之间的定价博弈模型.利用统计学中的多元线性回归模型给出两种不同型号汽车的销售量和价格的经验的需求函数关系式,检验了此模型的拟合优度,对其整体显著性的进行了F检验,并对偏回归系数的显著性进行了t检验,探讨了两寡头垄断企业的产品的需求函数为二元线性函数的伯特兰德模型,获得了其纳什均衡解的一般结论,并给出了某两型号汽车的定价博弈的具体均衡结果.     

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.     

求解随机广义纳什均衡问题的样本均值方法

研究随机广义纳什均衡问题.给出了随机广义纳什均衡问题变分不等式形式的再定式.利用期望残差最小化方法,获得了求解该问题的一种新的模型.并通过拟蒙特卡罗方法给出了该模型的求解方法.     

考虑直销的多期供应链网络均衡模型

研究了直销供应链网络动态均衡模型,分别对制造商、零售商和需求市场的决策者的多期独立决策行为及其相互作用进行了分析,利用变分不等式构建了各层均衡模型以及系统均衡模型,得到了系统达到均衡的条件,给出了具体算例并进行了求解.构建的供应链网络动态均衡模型具有更好的适用性及普遍性,为供应链的各层成员保持供应链的稳定和长期均衡提供决策依据和决策方法.     

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.     

完备市场下的均衡和财富优化

针对跳扩散模型中的优化与均衡问题,利用鞅方法和随机点过程理论,建立了跳扩散模型下的均衡市场,分析了市场中的财富优化问题,给出了均衡大宗商品现货价格、最优财富过程、最优投资组合及最优消费过程.     

随机需求下直销多商品流供应链网络均衡模型

建立了随机需求下直销多商品流供应链网络均衡模型,导出了供应链网络达到均衡的条件,它等价于一个有限维变分不等式.通过构建修改拟牛顿法,获得了随机需求下直销多商品流供应链网络均衡模型的解(变分不等式的解),并给出了1个算例,验证了模型的正确性和算法的可行性.     

Global bifurcation of positive equilibria in nonlinear population models

Existence of nontrivial nonnegative equilibrium solutions for age-structured population models with nonlinear diffusion is investigated. Introducing a parameter measuring the intensity of the fertility, global bifurcation is shown of a branch of positive equilibrium solutions emanating from the trivial equilibrium. Moreover, for the parameter-independent model we establish existence of positive equilibria by means of a fixed point theorem for conical shells.     

Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models

In this paper we are concerned with the fractional-order predator-prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibrium point is a centre for the integer order system but locally asymptotically stable for its fractional-order counterpart.     

Stochastic Variational Inequality Approaches to the Stochastic Generalized Nash Equilibrium with Shared Constraints

In this paper, we consider the generalized Nash equilibrium with shared constraints in the stochastic environment, and we call it the stochastic generalized Nash equilibrium. The stochastic variational inequalities are employed to solve this kind of problems, and the expected residual minimization model and the conditional value-at-risk formulations defined by the residual function for the stochastic variational inequalities are discussed. We show the risk for different kinds of solutions for the stochastic generalized Nash equilibrium by the conditional value-at-risk formulations. The properties of the stochastic quadratic generalized Nash equilibrium are shown. The smoothing approximations for the expected residual minimization formulation and the conditional value-at-risk formulation are employed. Moreover, we establish the gradient consistency for the measurable smoothing functions and the integrable functions under some suitable conditions, and we also analyze the properties of the formulations. Numerical results for the applications arising from the electricity market model illustrate that the solutions for the stochastic generalized Nash equilibrium given by the ERM model have good properties, such as robustness, low risk and so on.     

Regularity of the solutions for micro-macro models near equilibrium

In this paper, we study the regularity of solutions to two microscopic-macroscopic models: Hookean spring model and FENE dumbbell model. By making use of the structure of Fokker-Planck operator and establishing the general Hardy-Littlewood's inequality, we show that the classical solutions near the equilibrium obtained in [F. Lin, C. Liu, Ping Zhang, On a micro-macro model for polymeric fluids near equilibrium, Comm. Pure Appl. Math. 60 (6) (2007) 838-866] and [F. Lin, Ping Zhang, The FENE dumbbell model near equilibrium, Acta Math. Sinica (Chin. Ser.) 24 (2008) 529-538] become smooth with respect to the end-to-end vector variable q for any positive time.     

比率依赖型捕食者-食饵系统行波解的存在性

本文讨论一类比率依赖型捕食者 -食饵系统的反应扩散方程组 .首先 ,我们证明了时间周期定常解的存在性和稳定性 .其次 ,我们给出了扩散引起正常数平衡解失稳的条件 .最后 ,我们证明了比率依赖型捕食者 -食饵系统行波解的存在性和渐近性 .     

Scalarization and optimality conditions for vector equilibrium problems

In this paper, we investigated vector equilibrium problems and gave the scalarization results for weakly efficient solutions, Henig efficient solutions, and globally efficient solutions to the vector equilibrium problems without the convexity assumption. Using nonsmooth analysis and the scalarization results, we provided the necessary conditions for weakly efficient solutions, Henig efficient solutions, globally efficient solutions, and superefficient solutions to vector equilibrium problems. By the assumption of convexity, we gave sufficient conditions for those solutions. As applications, we gave the necessary and sufficient conditions for corresponding solutions to vector variational inequalities and vector optimization problems.     

Global asymptotic behaviour for a Nicholson model with patch structure and multiple delays

For a Nicholson’s blowflies model with patch structure and multiple discrete delays, we study some aspects of its global dynamics. Conditions for the absolute global asymptotic stability of both the trivial equilibrium and a positive equilibrium (when it exists) are given. The existence of positive heteroclinic solutions connecting the two equilibria is also addressed. We further consider a diffusive Nicholson-type model with patch structure, and establish a criterion for the existence of positive travelling wave solutions, for large wave speeds. Several applications illustrate the results, improving some criteria in the recent literature.     

具有多平衡解的种群模型平衡解的吸收域

考虑具有多平衡解的种群动力系统模型 ,在讨论各平衡解渐近性质的基础上 ,通过对种群育龄区间的分析 ,证明了平衡解对初值的连续依赖性 ,给出了各平衡解的吸收域 .     

半导体中一维拟中性飘流扩散模型整体光滑解的渐近性

In this paper, we study the asymptotic behavior of globally smooth solutions of initial boundary value problem for 1-d quasineutral drift-diffusion model for semiconductors. We prove that the smooth solutions(close to equilibrium)of the problem converge to the unique stationary solution.     

Dynamics of a delayed business cycle model with general investment function

The aim of this paper is to study the dynamics of a delayed business cycle model with general investment function. The model describes the interaction of the gross product and capital stock. Furthermore, the delay represents the time between the decision of investment and implementation. Firstly, we show that the model is well posed by proving the global existence and boundedness of solutions. Secondly, we determine the economic equilibrium of the model. By analyzing the characteristic equation, we investigate the stability of the economic equilibrium and the local existence of Hopf bifurcation. Also, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theory. Moreover, the global existence of bifurcating periodic solutions is established by using the global Hopf bifurcation theory. Finally, our theoretical results are illustrated with some numerical simulations.