数学规划方法确定的最优生产函数的性质

§1.最优生产函数的存在性 令R_+~n={(x_1,…,x_n)|x_i≥0,i=},设生产过程的投入向量为x∈XR_+~n(X为投入可能集),产出向量为y∈R_+~m,已知生产活动观测集为:={(x~1,y~1),…,(x~N,y~N)}其中x~i∈R_+~n,y~i∈R_+~m,x~i≠0(0,0),i=,那么由诱导的生产可能集为:     

The optimal control for promoting the cooperation in evolution game generated by Prisoner's Dilemma

Natural selection opposes the evolution of cooperation unless specific mechanisms are at work in Prisoner's Dilemma. By taking advantage of the modern control theory, the controller design is discussed and the optimal control is designed for promoting cooperation based on the recent advances in mechanisms for the evolution of cooperation. Two control strategies are proposed: compensation control strategy for the cooperator when playing against a defector and reward control strategy for cooperator when playing against a cooperator. The feasibility and effectiveness of these control strategies for promoting cooperation in different stages are analyzed. The reward for cooperation can't prevent defection from being evolutionary stable strategy (ESS). On the other hand, compensation for the cooperator can't prevent defection from emerging and sustaining. By considering the effect and the cost, an optimal control scheme with constraint on the admissible control set is put forward. By analyzing the special nonlinear system of replicator dynamics, the exact analytic solution of the optimal control scheme is obtained based on the maximum principle. Finally, the effectiveness of the proposed method is illustrated by examples.     

网络外部性条件下差异化双边平台买者参与问题

双边平台存在的基础是参与的用户,因此用户的分配是双边市场上各利益主体最关心的问题。为研究用户分配问题,本文在具有差异性的竞争双边市场上,建立了两阶段的双边平台竞争模型。第一阶段使用Rubinstein讨价还价模型对卖者的参与人数进行分配,利用讨价还价顺序描述卖者进入的先后顺序;第二阶段分别在平台利润最大化和社会福利最大化两种情况下,刻画买者对平台的规模偏好,并求均衡的市场份额。通过此模型分析竞争性平台差异化的情况下,网络外部性系数对平台均衡市场份额以及市场利益相关者利得的影响。研究表明:在考虑平台利润最大化的情况下,买者参与人数受卖者规模与网络外部性系数的影响,平台规模并非越大越好;在考虑社会福利最大化的情况下,买者的网络外部性系数与买者参与人数不相关,但与总社会福利正相关。     

基于AHP-GRA的湖北省科技创新人才开发评价研究

科技创新人才是推动经济社会发展的核心资源,是提升一个区域乃至一个国家核心竞争力的关键所在.以科技创新人才开发为核心,从人才可持续发展的视角,建立一套衡量湖北省科技创新人才开发水平的评价指标体系,同时结合层次分析法(AHP)和灰色关联分析法(GRA)构建评价模型,对湖北省科技创新人才开发水平及发展态势进行实证分析,探索提高湖北省科技创新人才开发水平的对策建议,为湖北省制定科技人才开发战略以及加强科技人才队伍建设提供决策参考.     

低碳视角下企业技术创新能力评价指标体系构建及评价研究

技术创新是企业在解决环保问题的同时保持经济绩效的重要途径,也是企业实现可持续发展的重要基础.以技术创新能力为研究主线,从低碳的视角,建立一套企业技术创新能力评价指标体系.该指标体系由技术创新投入能力、技术创新产出能力、技术创新研发能力和技术创新管理能力4项主体指标和16项个体指标构成.同时,结合层次分析法(AHP)和模糊综合评判法(FCE)构建综合评价模型,并进行实证分析,为政府和企业制定相关政策提供决策参考.     

Evolutionary games in a generalized Moran process with arbitrary selection strength and mutation

By using a generalized fitness-dependent Moran process, an evolutionary model for symmetric 2×2 games in a well-mixed population with a finite size is investigated. In the model, the individuals' payoff accumulating from games is mapped into fitness using an exponent function. Both selection strength β and mutation rate ε are considered. The process is an ergodic birth-death process. Based on the limit distribution of the process, we give the analysis results for which strategy will be favoured when ε is small enough. The results depend on not only the payoff matrix of the game, but also on the population size. Especially, we prove that natural selection favours the strategy which is risk-dominant when the population size is large enough. For arbitrary β and ε values, the 'Hawk--Dove' game and the 'Coordinate' game are used to illustrate our model. We give the evolutionary stable strategy (ESS) of the games and compare the results with those of the replicator dynamics in the infinite population. The results are determined by simulation experiments.     

THE AVERAGE ABUNDANCE FUNCTION WITH MUTATION OF THE MULTI-PLAYER SNOWDRIFT EVOLUTIONARY GAME MODEL

This article explores the characteristics of the average abundance function with mutation on the basis of the multi-player snowdrift evolutionary game model by analytical analysis and numerical simulation.The specific field of this research concerns the approximate expressions of the average abundance function with mutation on the basis of different levels of selection intensity and an analysis of the results of numerical simulation on the basis of the intuitive expression of the average abundance function.In addition,the biological background of this research lies in research on the effects of mutation,which is regarded as a biological concept and a disturbance to game behavior on the average abundance function.The mutation will make the evolutionary result get closer to the neutral drift state.It can be deduced that this affection is not only related to mutation,but also related to selection intensity and the gap between payoff and aspiration level.The main research findings contain four aspects.First,we have deduced the concrete expression of the expected payoff function.The asymptotic property and change trend of the expected payoff function has been basically obtained.In addition,the intuitive expression of the average abundance function with mutation has been obtained by taking the detailed balance condition as the point of penetration.It can be deduced that the effect of mutation is to make the average abundance function get close to 1/2.In addition,this affection is related to selection intensity and the gap.Secondly,the first-order Taylor expansion of the average abundance function has been deduced for when selection intensity is sufficiently small.The expression of the average abundance function with mutation can be simplified from a composite function to a linear function because of this Taylor expansion.This finding will play a significant role when analyzing the results of the numerical simulation.Thirdly,we have obtained the approximate expressions of the average abundance function corresponding to small and large selection intensity.The significance of the above approximate analysis lies in that we have grasped the basic characteristics of the effect of mutation.The effect is slight and can be neglected when mutation is very small.In addition,the effect begins to increase when mutation rises,and this effect will become more remarkable with the increase of selection intensity.Fourthly,we have explored the influences of parameters on the average abundance function with mutation through numerical simulation.In addition,the corresponding results have been explained on the basis of the expected payoff function.It can be deduced that the influences of parameters on the average abundance function with mutation will be slim when selection intensity is small.Moreover,the corresponding explanation is related to the first-order Taylor expansion.Furthermore,the influences will become notable when selection intensity is large.     

基于混合支持向量机的国防R&D项目中止决策方法

由于RD活动的高风险性,对国防RD项目开展中止决策研究具有重要的理论和现实意义.将传统RD项目中止决策的解决途径分为两类:分类型和回归型.在分析这两种解决途径存在不足的情况下,考虑到国防RD项目自身的特点,提出一种基于混合支持向量机(support vector machine,SVM)的项目中止决策方法;同时,针对模型的建立问题,提出采用交叉验证的方法,通过粒子群优化(particle swarm optimization,PSO)算法实现模型的优化选择.通过建立混合决策模型,可以得出项目中止决策的明确结论.应用分析表明,该方法能够同时实现对项目的分类和排序,较常用方法利用信息更为全面,得出结论更为细致,对实践中的项目中止决策具有较好的适应性.     

湖北省农业现代化评价指标体系构建及评价研究

在分析农业现代化评价研究现状和进展的基础上,参考和借鉴国内外最新研究成果,提出湖北省农业现代化评价指标体系和评价方法.指标体系由农村社会发展水平、农业投入水平、农业产出水平和农业可持续发展水平4项主体指标和16项个体指标构成.同时,运用唯一参照物比较判断法(G_2-法)和Delphi法相结合确定指标权重,并在此基础上采用多指标综合测度法构建评价模型,对湖北省不同水平年的农业现代化建设水平及发展态势进行实证分析,探索提高湖北省农业现代化建设水平的对策建议,为湖北省农业现代化发展提供决策参考.