基于拟生灭过程的随机支付2×2双矩阵博弈演化模型

引入分位数定义了随机支付值的偏好,并在此偏好的基础上定义带随机支付双矩阵博弈的纳什均衡.建立了有限种群进行带随机支付2×2双矩阵博弈的演化博弈模型,应用有限状态空间的拟生灭过程刻画了在有随机扰动的博弈环境中有限理性个体的学习调整动态,描述了理性演化的不确定性过程,讨论了拟生灭过程的平稳分布与演化模型的长期均衡以及博弈的纳什均衡之间的关系.最后,基于分块矩阵的Guass消去法给出求解模型稳态分布的数值算法,并通过数值实例对演化博弈模型均衡解的实现进行了说明.     

Evolutionary Game Model of 2 × 2 Stochastic Bimatrix Game based on Quasi Birth and Death Process

In this article, the preferences for stochastic payoffs are defined by quantile, and the definition of Nash equilibrium of the stochastic bimatrix game is given based on the preferences. Then the bimatrix game with stochastic payoffs is modeled as a finite, state-dependent quasi birth and death process, to describe the adjust dynamic in the game, with perturbations. The relations between the steady-state probabilities of the quasi birth and death process and Nash equilibrium are discussed by the evolutionary game model. In addition, an efficient numerical method based on block Gaussian elimination is proposed to compute the steady-state probabilities, and some examples as well as numerical results are given to prove its efficiency.     

研发操纵、”多赢困境“与有效监管——随机演化博弈模型与仿真

围绕高新技术企业申报中存在的研发操纵现象,构建地方政府、申报企业和中介机构的三方随机演化博弈模型,借鉴 随机微分方程理论分析博弈主体行为稳定性的条件,并运用计算机仿真分析了各关键变量对博弈主体策略选择的方向性及程度性影响。研究发现：一方面,企业上缴税收降低,申报企业研发操纵投机概率降低,这确认了企业减费降税对于提高企业创新真实性的积极影响;另一方面,中介机构的研发操纵成功概率与研发操纵行为选择概率成反比,低研发操纵成功概率反而会增强中介机构的研发操纵意愿。研究表明：企业在未获批高新技术企业前上缴税收的额度变化和获批高新技术企业后的减税比例,对博弈主体的策略选择影响均呈现方向性和程度性差异;进一步,确认了地方政府创新绩效提升会削弱其对研发操纵行为监管的积极性。此外,从监管效率看,政府采取举措提高企业单独进行研发操纵成本比提高中介进行研发操纵成本效果更显著。     

基于随机演化博弈的战略联盟稳定性分析和仿真

借助演化博弈论考虑了大群体成员下的战略联盟成员策略演化过程,建立了复制动态方程.指出了现有的确定性动态方程的不足,从人群工作互动角度探讨了策略演化过程中扰动的来源,在此基础上,对方程引入白噪声来反映过程所受到的随机干扰,建立了随机动力系统,借鉴 Itô 随机微分方程理论来分析战略联盟演化过程中成员行为稳定性的问题.给出了联盟保持稳定的一个充分条件和解体的一个充分条件,以此来解释战略联盟的有效性问题.利用计算机进行了仿真,针对结果将本模型与现有确定性的动力模型进行了比较,两次仿真实验测度了联盟演化的随机动力模型的有效性.     

A BSDE Approach to Stochastic Differential Games Involving Impulse Controls and HJBI Equation

This paper focuses on zero-sum stochastic differential games in the framework of forward-backward stochastic differential equations on a finite time horizon with both players adopting impulse controls. By means of BSDE methods, in particular that of the notion from Peng’s stochastic backward semigroups, the authors prove a dynamic programming principle for both the upper and the lower value functions of the game. The upper and the lower value functions are then shown to be the unique viscosity solutions of the Hamilton-Jacobi-Bellman-Isaacs equations with a double-obstacle. As a consequence, the uniqueness implies that the upper and lower value functions coincide and the game admits a value.

     

选择差异下Moran过程的随机博弈模型及其应用

研究有限种群中2×2的对称博弈,假设采取不同策略的个体具有不同的选择强度,建立选择差异下Moran更新过程的随机博弈模型.利用扩散近似的方法得到选择差异下Moran过程策略的扎根概率,扎根概率不仅与博弈收益矩阵和种群的大小相关,还与策略的差异选择强度相关.通过比较弱选择和中性选择下策略的扎根概率,分析自然选择有利于策略在种群中扎根及策略成为演化稳定策略的条件.在常见的三种博弈:囚徒困境,共存博弈和协调博弈中,利用数值分析方法,得到扎根概率与选择强度及种群大小之间的关系;利用仿真方法得到扎根时间与选择强度之间的关系.最后将选择差异下的Moran过程随机博弈模型,应用于解决第三方物流企业是否参与供应链金融的策略选择问题.求解第三方物流企业参与供应链金融策略的扎根概率,分析有利于参与策略扎根及参与策略成为演化稳定策略的条件,利用数值和仿真分析方法得到各参数变化对第三方物流企业博弈行为的影响.本文的研究内容扩展了Moran更新过程的随机演化博弈理论.     

模糊联盟的Shapley值与稳定性

基于经典合作博弈Shapley值的概念及模糊合作博弈理论, 给出了具有模糊联盟的合作博弈个体理性及集体理性定义. 基于Butnariu提出的具有比例值的模糊博弈及Tsurumi提出的具有Choquet积分形式的模糊博弈, 结合 Li 提出的Shapley函数的简化表达式, 研究了模糊联盟的稳定性问题, 证明了一些相关结论.     

岛屿争端中国家间博弈模型与策略仿真分析

岛屿争端通常涉及国家的核心利益及国际形象,根据岛屿争端问题的特点和相关国家可能采取的行为,研究了针对岛屿争端问题的国家间博弈模型,并对相关国家的策略进行了仿真分析。首先,将主动型国家和被动型国家的行为交互描述为一个随机博弈,并建立相应的博弈模型;然后,应用该模型分析主动型国家的期望行为和被动型国家的防守行为;最后,用计算机仿真分析相关国家的行为能力变化时对其策略选择和最终收益的影响。研究成果将为有岛屿争端问题的相关国家制定策略时提供有益的参考。     

A Mean-Field Linear-Quadratic Stochastic Stackelberg Differential Game with one Leader and Two Followers

This paper is concerned with a linear-quadratic(LQ) stochastic Stackelberg differential game with one leader and two followers, where the game system is governed by a mean-field stochastic differential equation(MF-SDE). By maximum principle and verification theorem, the open-loop Stackelberg solution is expressed as a feedback form of the state and its mean with the help of three systems of Riccati equations.     

基于次序统计量的发电公司竞价策略研究

假定竞争对手的报价策略变量服从某种经验分布,基于贝叶斯博弈原理,运用次序统计量方法,分别对电力需求确定与不确定情况下的发电公司竞价构造了博弈模型,并通过模型的求解与分析,给出了发电公司的均衡报价策略;最后对由5个发电商组成的电力竞价市场进行了算例分析,结果表明:发电商的均衡报价要么接近报价上限,要么在较低价格水平上随成本呈正向变动.     

不确定性矩阵对策解的确定

本文研究了五个问题：１．具有精确策略和模糊值对策矩阵的对策解的确定；２．具有模糊策略和经典对策矩阵的对策解的确定；３．具有模糊策略和函数值对策矩阵对策解的确定；４．具有模糊随机策略和经典对策矩阵对策解的确定；５．具有模糊随机策略和函数值对策矩阵对策解的确定。     

Backward linear-quadratic stochastic optimal control and nonzero-sum differential game problem with random jumps

This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps. The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations. The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed. All these results develop those of Lim, Zhou (2001) and Yu, Ji (2008).     

Maximum Principle for Non-Zero Sum Stochastic Differential Game with Discrete and Distributed Delays

This technical note is concerned with the maximum principle for a non-zero sum stochastic differential game with discrete and distributed delays. Not only the state variable, but also control variables of players involve discrete and distributed delays. By virtue of the duality method and the generalized anticipated backward stochastic differential equations, the author establishes a necessary maximum principle and a sufficient verification theorem. To explain theoretical results, the author applies them to a dynamic advertising game problem.     

Delay-dependent exponential stability of impulsive stochastic systems with time-varying delay

The problem of delay-dependent exponential stability is investigated for impulsive stochastic systems with time-varying delay.Although the exponential stability of impulsive stochastic delay systems has been discussed by several authors,few works have been done on delay-dependent exponential stability of impulsive stochastic delay systems.Firstly,the Lyapunov-Krasovskii functional method combing the free-weighting matrix approach is applied to investigate this problem.Some delay-dependent mean square exponential stability criteria are derived in terms of linear matrix inequalities.In particular,the estimate of the exponential convergence rate is also provided,which depends on system parameters and impulsive effects.The obtained results show that the system will stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous flows,and impulses may be used as controllers to stabilize the underlying stochastic system.Numerical examples are given to show the effectiveness of the results.     

随机回收下的逆向供应链协调

逆向供应链中,再制造商将废旧产品的回收外包给专门的回收商,回收商获得废旧产品的数量是与回收价格相关的随机变量．再制造商首先提供合同,然后回收商基于合同作出反应来决策回收价格,双方的目标是在随机回收环境下最大化各自的期望利润．利用博弈论和优化理论,分别得到了分散式和集中式供应链系统下的最优决策,并证明了批发价合同下的双边效应在逆向供应链中仍然存在．然后给出了供应链的协调机制——“双阶段定价合同”．最后通过数值仿真验证了所得结果的有效性．     

产品差异下的策略投资

在产品差异的情况下, 消费者对各公司产品偏好不同从而公司定价优势也不同. 以市场需求和定价优势为随机变量, 建立了一个非对称双寡头期权博弈模型来研究异质公司的策略投资问题. 推导出抢占投资阈值存在的条件, 并根据其存在情况分析出子博弈纳什均衡策略. 研究发现: 需求下降诱发过度开发的现象除了因抢占市场所致外, 还可能由公司定价优势更大程度的增加引起. 此外, 就相关参数对投资阈值的影响做了比较静态与敏感性分析, 为公司的投资行为提供一定的理论依据和实践指导.     

Moment Equations of Linear It Stochastic Systems with Applications

1.INTRODUCTIONAsiswellknown,stochasticsystemmodeloftheIt6typeisoneofthemostimportantmodelsforstochasticsystems,manystochasticsystemswithcolorednoisecanbestudiedwithhelpoftheIt6stochasticsystems[if.ForthestabilityandcontrolproblemofIt6stochasticsystems,nlallyresultshavebeenobtainedintheliteratures[l~6].Whilesomebasicproblems,suchasthenecessaryandsufficientconditionofmean-squarestabilityoflinearIt6stochasticsystems,havehotbeensolved.Inthepreviousliterature,someresultsonthestabilityoflinear…     

State and Output Feedback Finite-time Guaranteed Cost Control of Linear It Stochastic Systems

The problem of guaranteed cost control based on finite-time stability for stochastic system is first investigated in this paper.The motivation of solving this problem arises from an observation that finite/infinite-horizon guaranteed cost control does not consider the transient performance of the closed-loop system,but guaranteed cost control based on finite-time stability involves this practical requirement.In order to explain this problem explicitly,a concept of the stochastic finite-time guaranteed cost control is introduced,and then some new sufficient conditions for the existence of state and output feedback finite-time guaranteed cost controllers are derived,which guarantee finite-time stochastic stability of closed-loop systems and an upper bound of a quadratic cost function.Furthermore,this problem is reduced to a convex optimization problem with matrix inequality constraints and a new solving algorithm is given.Finally,an example is given to illustrate the effectiveness of the proposed method.     

Analyses of location-price game on networks with stochastic customer behavior and its heuristic algorithm

<正> In this paper,a two-stage model is developed to investigate the location strategy andthe commodity pricing strategy for a retail firm that wants to enter a spatial market with multiplecompetitive facilities,where a competitor firm is already operating as a monopoly with several outlets.Expected market shares are calculated based on the stochastic customer behavior on networks.Theauthors provide a sufficient condition for the existence of equilibrium prices in the price game for thefirst time.The existence and uniqueness of the pure strategy Nash equilibrium price with a specifiedutility function are proved in the subgame.A metaheuristic based on tabu search is proposed tosearch the optimal location-price solution of the model.In addition,the authors provide two numericalexamples to illustrate how to obtain the optimal solution and conduct sensitivity analysis.The analysisshows that the best location decision is robust for the follower firm,price game is more intense whenincomes of consumers are lower or there are more substitution products,and neither chain retail gainsfrom the price competition.     

具有惩罚策略的公共物品博弈与合作演化

采用演化博弈方法,研究具有代价的第二方惩罚机制对于公共物品博弈均衡选择及群体合作行为的影响.将群体策略选择过程描述成一个多维马氏过程,通过极限分布分析系统演化稳定状态.分别考虑只对背叛策略进行惩罚的一阶惩罚机制和同时对背叛及不惩罚背叛的合作(二阶背叛)都进行惩罚的二阶惩罚机制.研究发现,与一阶惩罚相比,二阶惩罚机制可以在更大参数范围内促进群体合作的产生,系统存在选择不同均衡结果的惩罚参数临界值.并将结果与复制动态模型进行了对比.