单主多从博弈中中级社会Nash均衡的存在性与应用

对单主多从博弈进行分析,给出跟随者反应函数的相关性质.进一步,针对跟随者反应函数是集值映射的情形,定义出中级社会Nash均衡,讨论该均衡的存在性,并把该均衡应用到非线性反需求函数的单主多从寡头竞争,得出该模型的中级社会Nash均衡解.     

反需求函数集值情况下单主多从寡头竞争模型

现实中反需求函数可能不是单值的,而是集值的.在这种情况下,研究单主多从寡头竞争模型。对集值反需求函数进行分析,给出跟随寡头的反应函数性质,证明模型Stackelberg-Cournot Nash均衡(SCN均衡)的存在性。     

不完全信息多维Cournot模型及其分析

根据现实中的博弈现象,本文首先提出了多维博弈概念,然后描述了其特征、策略型式,并将Nash均衡扩展为多维Nash均衡．最后,讨论了两个企业关于具有一定替代性的两种产品的不完全信息静态多维Cournot多维博弈模型,并进一步分析得到两个企业对两种产品单独博弈的均衡策略劣于对两种产品多维博弈的均衡策略．     

复杂产业网络上的技术创新博弈扩散研究

创新的价值在于扩散,但扩散依赖于路径选择与扩散规则.提出了技术创新扩散的一对多博弈模型,并求解出了Nash均衡解.Nash均衡表明,传播者采取扩散策略的概率与学习者的学习成本和拒绝代价之差成正比;学习者采取学习策略的概率不但与传播者的封锁成本成正比,而且与网络的平均度成正比;进而,基于马尔科夫链的吸收态,进一步分析了产业网络上技术创新博弈扩散的平均步数;基于平均场理论,分析了产业网络上技术创新博弈扩散的分布及其分布密度.最后,通过长三角IC产业网络给出了实证分析.     

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.     

基于差异化产品动态寡头博弈的系统动力学分析

以寡头企业具有有限理性和简单理性的产量调整行为和非线性成本函数为基础,论证了当横向产品差异度在一定范围内时,纳什均衡可作为稳定的动态均衡而实现.当超过一定范围时,利用数值模拟可观测到系统出现的周期性和混沌的复杂现象.在企业具有二次成本的假设条件下,研究了产品差异程度对纳什均衡稳定性的影响,得到了产品差异度越大,或市场竞争程度越低,系统的纳什均衡越不稳定的结论,表明了经济周期波动产生于非线性系统的内生性.与线性成本的对比说明,非线性成本缩小了纳什均衡的稳定域,增加了寡头市场的复杂性.研究也表明规模不经济的寡头厂商想通过增加产品差异度来减少竞争是有一定难度的.     

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.     

有限理性双寡头博弈模型的复杂性分析

以Bowley博弈模型为核心,将寡头的调整速度作为企业的竞争策略,并对该模型Nash均衡点的稳定域进行分析;通过数值仿真把双寡头的策略区域分为均衡区、周期区和混沌区。研究发现双寡头博弈市场中,寡头为了获得更大的利润而不断改变自身产量策略,这是市场出现周期波动、甚至陷入混沌的根本内因.     

古诺竞争的选址模型研究

在Paul提出的圆环形城市模型基础上,通过引入成本分布函数,扩展了Pal和Matsushima的模型,建立了一个新的带有成本因子的选址与产量竞争的双寡头竞争模型.结果表明:如果成本分布函数是常数,那么两企业均衡地分布于圆环形城市将达到完美的纳什均衡;如果成本分布函数是严格凸函数,当运输系数较小时,企业将在产品成本分布函数最小点处集聚,并各自达到利润最大化.     

数字环境下产品定价与一种产品差异化机制模型分析

本文首先分析了在新的市空下市场结构特征和厂商定价策略,以及价格机制的演变和不同市场环境下具体价格机制的使用;依据逆向选择原理,设计了一种有中间商参与的基于顾客需求和品牌偏好的产品差别定价机制模型,利用logit模型得到厂商利润方程;然后对模型性质以及厂商间产品价格、产品特性的影响进行了分析,得出厂商定价策略必存在Nash均衡,并对两种情形下如何求均衡解进行了说明;最后对参数估计进行了分析。     

On Nash–Cournot oligopolistic market equilibrium models with concave cost functions

We consider Nash–Cournot oligopolistic market equilibrium models with concave cost functions. Concavity implies, in general, that a local equilibrium point is not necessarily a global one. We give conditions for existence of global equilibrium points. We then propose an algorithm for finding a global equilibrium point or for detecting that the problem is unsolvable. Numerical experiments on some randomly generated data show efficiency of the proposed algorithm.     

不完全信息下动态库诺特模型的均衡分析

本文通过引入厂商成本类型的预测概率建立了动态库诺特模型,分析了其对最优均衡产量以及利润的影响,得出了一些具有指导意义的结论.     

Stability of the Cournot equilibrium for a Cournot oligopoly model with n competitors

In this paper a Cournot-like model is constructed with an iso-elastic demand function for n competitors. The Cournot equilibrium is constructed for general constant unit costs. Finally, it is proved that for identical unit costs the Cournot point is a sink for two or three competitors and a saddle for more than four players.     

Complex dynamic properties of Cournot duopoly games with convex and log-concave demand function

A Cournot duopoly game is proposed where the interdependence between firms depends on convex and log-concave demand function. In this paper, a model of two rational firms that are in competition and produce homogeneous commodities is introduced. The equilibrium points of this model are obtained and their dynamical characteristics such as stability, bifurcation and chaos are investigated. Furthermore, a multi-team Cournot game is introduced. Through simulation the dynamical characteristics of the equilibrium points of this game are illustrated.     

Oligopoly models for market price of electricity under demand uncertainty and unit reliability

Several oligopoly models have been proposed for representing strategic behavior in electricity markets, which include Bertrand, Cournot, and Supply Function Equilibrium (SFE). For the most part, these models are deterministic, with the exception of the SFE originally developed by Klemperer and Meyer. However, their model does not include supply side uncertainties. In this paper, we consider both load and supply side uncertainties (resulting from generator availabilities). We obtain Nash equilibrium solutions for Cournot and SFE models, in which asymmetric firms (whose generating units have different costs and capacities) submit their bids so that each firm’s expected profit is maximized.     

A Projected Subgradient Algorithm for Bilevel Equilibrium Problems and Applications

In this paper, we propose a new algorithm for solving a bilevel equilibrium problem in a real Hilbert space. In contrast to most other projection-type algorithms, which require to solve subproblems at each iteration, the subgradient method proposed in this paper requires only to calculate, at each iteration, two subgradients of convex functions and one projection onto a convex set. Hence, our algorithm has a low computational cost. We prove a strong convergence theorem for the proposed algorithm and apply it for solving the equilibrium problem over the fixed point set of a nonexpansive mapping. Some numerical experiments and comparisons are given to illustrate our results. Also, an application to Nash–Cournot equilibrium models of a semioligopolistic market is presented.     

Analysis of the dynamics of Cournot team-game with heterogeneous players

In this paper, we study a dynamical system of a two-team Cournot game played by a team consisting of two firms with bounded rationality and a team consisting of one firm with naive expectation. The equilibrium solutions and the conditions of their locally asymptotic stability are studied. It is demonstrated that, as some parameters in the model are varied, the stability of the equilibrium will get lost and many such complex behaviors as the period bifurcation, chaotic phenomenon, periodic windows, strange attractor and unpredictable trajectories will occur. The great influence of the model parameters on the speed of convergence to the equilibrium is also shown with numerical analysis.     

Equilibrium path in oligopolistic market of nonrenewable resource

In this paper we study the oligopoly model of nonrenewable resource in which the unit production cost is variable and depends on the resource reserve level. We consider both the open-loop strategy and the closed-loop strategy of this dynamical differential game. For the case of linear cost function we have observed that the open-loop equilibrium and the self-feedback equilibrium satisfy the same equilibrium conditions, which can be described as a dynamical system. The analysis shows that the equilibrium path of the model is the stable orbit of this system, and this result leads to further studies of the properties of the total extraction and reserve and the individual ones of each producer. For the total extraction rate and reserve, some of the properties are similar to those of most oligopoly models with fixed unit production cost. For the individual behaviors, we have found out the solution expressions of the individual extraction rate and resource reserve and got the main result that the producer with larger initial stock has a larger but declining market share and the share of each producer converges toward the average one when time approaches to infinite.     

Oligopoly games under asymmetric costs and an application to energy production

Oligopolies in which firms have different costs of production have been relatively under-studied. In contrast to models with symmetric costs, some firms may be inactive in equilibrium. (With symmetric costs, the results trivialize to all firms active or all firms inactive.) We concentrate on the linear demand structure with constant marginal but asymmetric costs. In static one-period models, we compare the number of active firms, i.e. the number of firms producing a positive quantity in equilibrium, across four different models of oligopoly: Cournot and Bertrand with homogeneous or differentiated goods. When firms have different costs, we show that, for fixed good type, Cournot always results in more active firms than Bertrand. Moreover, with a fixed market type, differentiated goods result in more active firms than homogeneous goods. In dynamic models, asymmetric costs induce different entry times into the market. We illustrate with a model of energy production in which multiple producers from costly but inexhaustible alternative sources such as solar or wind compete in a Cournot market against an oil producer with exhaustible supply.     

基于博弈论视角的稀土矿区环境治理及监管策略研究

针对稀土矿区环境治理的复杂性,本文通过建立地方政府和稀土企业之间的动态演化博弈模型,分析了博弈双方在不同情形下的演化稳定策略及其影响因素,并利用matlab对其进行数值仿真。研究表明,地方政府的监管成本、执行环境规制时对稀土企业的奖惩政策、稀土企业的治污成本以及非法开采时的额外收益都会影响地方政府与稀土企业的演化稳定策略,降低地方政府的监管成本、稀土企业的治污成本等都会引导博弈双方的演化稳定策略趋向于{严格监管,合法开采},从而促进矿区环境的可持续性发展。