基于博弈论视角的农业电商区域品牌建设

农产品区域品牌的建立有利于买家在电商平台上对同类产品进行甄别,农产品区域品牌也是一个地区具有的区域特色农产品的"代言",对提升农产品竞争力、降低交易成本具有积极意义.但是农产品区域品牌又具有公共物品的属性,因此可能导致一些劣质产品出现"搭便车"的情况,必须通过一系列制度的建设来避免以次充好情况的出现,从而维护农产品区域品牌的品牌忠诚度和认同度,为农业电商的发展提供一个更有利的市场环境.     

带有下方风险控制的退休后最优投资决策

退休后最优投资决策经常采取目标定位模型.然而,传统的目标定位模型无法很好地控制下方风险,即事件“在未来时刻购买年金提供的消费水平低于在退休时刻购买年金提供的消费水平”发生概率较高.文章在传统的目标定位模型里引入安全第一准则,大大降低了下方风险发生概率.利用拉格朗日乘子法、动态规划方法和嵌入法得到了最优策略的半解析解.通过数值算例对比分析了传统目标定位模型和文章模型的下方风险发生概率、终身累计消费均值和破产事件发生次数的性质.     

一类变化区域中的粪口模型的传播动力学

为了研究空间区域的变化对粪口传染病的影响,构建了一类具有区域变化特征的粪口传播模型.通过下一代感染算子和相关特征值问题引出模型的基本再生数,作为判断疾病传播和消失的阈值,并利用比较原理和上下解方法探究解的长期行为.结果表明,区域的扩张会增加病毒的传播风险,不利于疾病的控制.最后,给出数值模拟和传染病学解释.     

不等式F（x）·（φ（x）)~(1/2)≥0解法探讨

引例解不等式 . 错解原不等式等价于不等式组: 即 解得x≥4, ∴ 原不等式的解集为{x|x≥4}. 剖析显然当x=-1时,原不等式也成立.为什么漏掉x=-1这个解呢?究其原因是忽略了原不等式中的“≥”号具有不等和相等的双重性.要注意:同解定理“不等式F(x) 与不等式组 同解”中的不等号是“>”,而不是“≥”.     

博弈论中的一个优化控制模型

博弈中往往会出现个人理性和集体理性的预选，使得社会资源不能得到很好的利用。本以公共悲剧为例，通过引入“政府”作为局中人，建立了一个特殊的完全信息动态博弈模型——带有控制的博弈模型。试图解决个人理性和集体理性的预选，实现对博弈均衡结果的优化。     

随机时滞 Lotka-Volterra 模型

该文揭示了关于生物动态过程中的一类重要的模型, 随机时滞Lotka-Volterra模型的渐近行为, 这种随机过程的解具有很好的逼近性质:如, 解的轨道估计, 渐近性质, 而且它的解还具有随机有界性.     

考虑事故风险损失的爆炸物品经济订货批量模型研究

爆炸物品在储存过程中存在发生爆炸事故,从而给人类和环境带来伤害的可能,因此在对爆炸物品进行采购决策时必需考虑由此带来的风险损失.在给出爆炸物品事故风险损失度量方法的基础上,建立了爆炸物品的经济订货批量模型,证明了模型存在唯一最优解,并给出了模型的求解步骤,为相关企业合理制定采购决策提供了理论依据.数字算例分析了事故概率、赔偿标准、单位库存费、单次采购费对最优批量的影响,比较了考虑事故风险损失与否时的最优批量,结果表明,当事故概率或赔偿标准较高时,两者对应的最优批量差异明显.这也说明,当事故概率或赔偿标准达到一定程度时,考虑事故风险损失是十分必要的.     

有政府干预的市场经济条件下收入及价格的变化对公共物品使用率的影响

本文根据有政府干预的市场经济的特点,假想公共物品在市场上达到了均衡,消费者在使用公共物品时,按其使用率支付相应的费用.建立了相应的数学模型,分析了当收入及价格发生变化时,对公共物品使用率的影响,具有一定的理论及应用价值.     

一类投资时点问题的最优停止模型及其等待时间

针对收益流与一次性投入沉淀成本均不确定的一类风险项目,为使其预期总的贴现净收益最大,提出了寻找项目最优投资时点的最优停止模型.这种方法不依赖于金融市场的完备性及市场无套利.借助于高切原理,通过求解一个自由边界问题,得到模型的候选解.运用最优停止理论证明了其的确为最优解,从而显式地给出了该类风险项目的最优投资时点.进一步,显式给出了到达最优时点的平均等待时间.     

投资的收益和风险的数学模型及算法研究

本文按照“满意解”、“多组解”的思路对投资的收益和风险问题进行了分析和处理 ,提出了将净收益与总体风险划分为若干等级 ,并按等级求出多组满意解的思想方法 ,最后对模型的数学性质与计算方法进行了初步研究     

阈值风险下的多企业合作治理污染的演化博弈分析

针对环境污染具有跨区域性,环境资源的公共物品属性,由单一产污企业治理污染物难以取得有效成果,辖区内多个产污企业合作治理是环境保护的必由之路。 本文从演化博弈论的研究视角探讨了多个排污企业之间的决策演化过程,建立了多主体演化博弈模型,并考虑了污染排放总量超过总量阈值时的环境恶化风险,研究阈值风险对产污企业合作治理污染策略选择的影响。 研究结果表明,较高的治理成本很大地约束了逐利企业治理污染的行为选择,造成公地悲剧的社会问题。 企业治污成本较大背景下,环境阈值风险发生概率越高,越能有效促进合作治理环境策略的演化稳定,合作治理占优于不治理。 出于对企业自身初始禀赋的保护,产污企业初始禀赋越大、排污收费率越高,越能有效促进企业治理污染物的积极性。 最后,为促进辖区内污染企业合作治理污染提出了政策建议。     

考虑供应链渠道冲突的零售商自有品牌产品定价方法

自有品牌产品定价是电子商务环境下零售商实施渠道管理的关键因素,其合理与否直接影响到零售商利润和供应链稳定.鉴于此,针对存在供应链渠道冲突的零售商自有品牌定价问题,从协调的角度,利用对偶理论与优化模型,构建了基于最小协调成本的零售商自有品牌产品定价决策方法,并利用其探讨协调的经济意义,求解零售商自有品牌产品最优定价.结果表明,所构建的模型能够有效描述和解决零售商自有品牌产品定价问题,并在一定程度上消除供应链渠道冲突,保证供应商和零售商长期有效合作和供应链可持续发展.     

Exchanging heterogeneous goods via sealed bid auctions and transportation systems

A primary commodity such as wheat, rice, coffee, oil, etc., is shipped fromm locations where it was grown or pumped ton manufacturers. Each manufacturer processes, packages, advertises, and distributes the commodity under a consumer product brand name. The resulting heterogeneous good is sold at a sealed bid auction, in competition with the other manufacturers of the consumer product, tok final customers. The problem to be considered in this paper is to find a way of determining prices for the goods produced and the physical exchanges between seller and buyer which satisfy flow conditions and which take into account the evaluations of the goods by both sellers and buyers. The first model for doing this is given in section 1, which combines the idea of a sealed bid auction due to Shapley, Shubik and Thompson, with a conventional transportation system. The sealed bid auction is used to determine the exchange prices, and the transportation system is used to calculate the production and transportation costs. It is suggested that the resulting model type can also be applied in a wide range of problems that arise in the marketing of goods sold under brand names (i.e., heterogeneous goods) regardless of whether they are actually exchanged at formal auctions. We show in section 6 that our model is a generalization of the transshipment model in a recent paper by Dubey and Shapley [1]. In their model they considered a number of oligopolists engaged in transshipping and trading goods. Their oligopolists set their prices in order to maximize profits, rather than having them determined by an auction process as is done in our model. In section 7, we extend the model to one in which the wholesalers are permitted to make positive profits. We show how to calculate the values of coalitions of the various players in the model.The work of the first named author was prepared as part of the activities of the Management Sciences Research Group, Carnegie Mellon University, under Contract No. N00014-85-K-0198 NR 047-048 with the Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

Investment under duality risk measure

One index satisfies the duality axiom if one agent, who is uniformly more risk-averse than another, accepts a gamble, the latter accepts any less risky gamble under the index. Aumann and Serrano (2008) show that only one index defined for so-called gambles satisfies the duality and positive homogeneity axioms. We call it a duality index. This paper extends the definition of duality index to all outcomes including all gambles, and considers a portfolio selection problem in a complete market, in which the agent’s target is to minimize the index of the utility of the relative investment outcome. By linking this problem to a series of Merton’s optimum consumption-like problems, the optimal solution is explicitly derived. It is shown that if the prior benchmark level is too high (which can be verified), then the investment risk will be beyond any agent’s risk tolerance. If the benchmark level is reasonable, then the optimal solution will be the same as that of one of the Merton’s series problems, but with a particular value of absolute risk aversion, which is given by an explicit algebraic equation as a part of the optimal solution. According to our result, it is riskier to achieve the same surplus profit in a stable market than in a less-stable market, which is consistent with the common financial intuition.     

Optimal routing of vehicles with communication capabilities in disasters

Major emergencies and disasters such as acts of terrorism, acts of nature, or human-caused accidents may lead to disruptions in traffic flow. Minimizing the negative effects of such disruptions is critical for a nation’s economy and security. A decision support system that is capable of gathering (real-time) information about the traffic conditions following a disaster and utilizing this information to generate alternative routes for vehicles would benefit the government, industry, and the public. For this purpose, we develop a mathematical programming model to minimize the delay for vehicles with communication capabilities following a disaster. Most commercial trucks and public buses utilize QUALCOMM as a communication tool. We also develop a prediction model for vehicles that do not have any communication capabilities. Although the problem is inherently integer we developed a linear program to reduce the computational burden caused by the large size of the problem. An algorithm is proposed to update the parameters of the linear program based on a duality analysis in order to obtain better results. A monotonic speed–density relationship is embedded in the model to capture high traffic congestion that occurs after a disaster. The model and the algorithm are tested using a simulated disaster scenario. The results indicate that the proposed model improves system performance measures such as mobility and average speed.     

Static duality and a stationary-action application

Conservative dynamical systems propagate as stationary points of the action functional. Using this representation, it has previously been demonstrated that one may obtain fundamental solutions for two-point boundary value problems for some classes of conservative systems via solution of an associated dynamic program. Further, such a fundamental solution may be represented as a set of solutions of differential Riccati equations (DREs), where the solutions may need to be propagated past escape times. Notions of “static duality” and “stat-quad duality” are developed, where the relationship between the two is loosely analogous to that between convex and semiconvex duality. Static duality is useful for smooth functionals where one may not be guaranteed of convexity or concavity. Some simple properties of this duality are examined, particularly commutativity. Application to stationary action is considered, which leads to propagation of DREs past escape times via propagation of stat-quad dual DREs.     

基于品牌价值的销售额预测模型应用研究

首先分析了企业的品牌价值与其销售额的变化情况,归纳出品牌价值与销售额之间的两个重要的变化规律.而后以此作为二者关系方程构建的基础假设,以广告反映模型(VW模型)为基础,将原模型中的广告投入变量替换为品牌价值变量,建立了品牌价值与销售额之间的关系方程.通过求解关系方程的平衡解,得到了以品牌价值为变量的销售额预测模型.最后,采用海尔集团的实际数据对所建模型的适用性和正确性进行了证明,同时还对模型的预测精度进行了检验.研究突破了以往研究一般采用时间、环境变量直接预测销售额,或是采用历史数据对销售额进行模拟预测等传统的预测方法,首次从品牌价值的角度出发研究其对销售额的影响途径及影响力度.品牌价值是能够包涵如广告投入等因素的全部信息量的重要指标,因此其能够更为全面客观地衡量商品在整个市场中的价值潜力、能够更准确地反映其未来的销售份额.     

“Bricks vs. Clicks”: The impact of manufacturer encroachment with a dealer leasing and selling of durable goods

In durable goods markets, many brand name manufacturers, including IBM, HP, Epson, and Lenovo, have adopted dual-channel supply chains to market their products. There is scant literature, however, addressing the product durability and its impact on players’ optimal strategies in a dual-channel supply chain. To fill this void, we consider a two-period dual-channel model in which a manufacturer sells a durable product directly through both a manufacturer-owned e-channel and an independent dealer who adopts a mix of selling and leasing to consumers. Our results show that the manufacturer begins encroaching into the market in Period 1, but the dealer starts withdrawing from the retail channel in Period 2. Moreover, as the direct selling cost decreases, the equilibrium quantities and wholesale prices become quite angular and often nonmonotonic. Among other results, we find that both the dealer and the supply chain may benefit from the manufacturer’s encroachment. Our results also indicate that both the market structure and the nature of competition have an important impact on the player’s (dealer’s) optimal choice of leasing and selling.