Oligopolistic contracting: Channel coordination under competition

We study contracts between a single retailer and multiple suppliers of two substitutable products, where suppliers have fixed capacities and present the retailer cost contracts for their supplies. After observing the contracts, the retailer decides how much capacity to purchase from each supplier, to maximize profits from the purchased capacity from the suppliers plus his possessed inventory (endowment). This is modeled as a noncooperative, nonzero‐sum game, where suppliers, or principals, move simultaneously as leaders and the retailer, the common agent, is the sole follower. We are interested in the form of the contracts in equilibrium, their effect on the total supply chain profit, and how the profit is split between the suppliers and the retailer. Under mild assumptions, we characterize the set of all equilibrium contracts and discuss all‐unit and marginal‐unit quantity discounts as special cases. We also show that the supply chain is coordinated in equilibrium with a unique profit split between the retailer and the suppliers. Each supplier's profit is equal to the marginal contribution of her capacity to supply chain profits in equilibrium. The retailer's profit is equal to the total revenue collected from the market minus the payments to the suppliers and the associated sales costs.     

Constant risk aversion in stochastic contests with exponential completion times

This article analyzes a class of stochastic contests among multiple players under risk‐averse exponential utility. In these contests, players compete over the completion of a task by simultaneously deciding on their investment, which determines how fast they complete the task. The completion time of the task for each player is assumed to be an exponentially distributed random variable with rate linear in the player's investment and the completion times of different players are assumed to be stochastically independent. The player that completes the task first earns a prize whereas the remaining players earn nothing. The article establishes a one‐to‐one correspondence between the Nash equilibrium of this contest with respect to risk‐averse exponential utilities and the nonnegative solution of a nonlinear equation. Using the properties of the latter, it proves the existence and the uniqueness of the Nash equilibrium, and provides an efficient method to compute it. It exploits the resulting representation of the equilibrium investments to determine the effects of risk aversion and the differences between the outcome of the Nash equilibrium and that of a centralized version.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:4–14, 2019     

一类非线性动力系统的定性分析

研究2种生物种群在一段时间内是否可以相互生存,有着重要的现实意义。为了获得这方 面的有关结果,本文运用微分方程的稳定性理论,详尽地讨论了一类非线性动力系统模型平衡点的类型, 并进一步给出了该系统极限环的不存在性,从而得到系统的共存性。     

一类流行病动力学模型的稳定性研究

本文建立了一类流行病动力学的S-I-D-S模型，讨论了该模型的无病平衡点的全局稳定性及有病平衡点的局部稳定性。     

李雅普诺夫运动稳定性与平衡状态稳定性的关系

稳定性是系统分析的重要内容 ,针对在系统稳定性分析中 ,运动稳定性和平衡状态稳定性之间常易于混淆的问题 ,详细分析了两种稳定性之间内在本质联系 ,给出了从一种稳定性过渡到另一种稳定性的方法     

空陆攻防博弈的动态武器目标分配

大规模作战具有高动态、非完全信息和不确定性，在分析归纳目前解决动态武器目标分配问题的一系列方法的基础上，尝试构建基于双方动态博弈的攻防对抗综合数学模型，并利用纳什均衡和帕累托最优算法进行分阶段求解。结果表明，该数学模型和博弈论方法结合能够有效解决武器目标动态分配问题。     

军事欺骗战法分析的数学方法-应用*

针对军事欺骗战法定量分析困难的问题,采用基于贝叶斯统计推断和博弈均衡分析的数学方法,在理论上为解决此难题提供了一种可行的方法.该方法首先定义基本概率矩阵,然后根据贝叶斯原理为交战双方构造用于统计推断的主观概率矩阵,并在由两个主观概率矩阵元素构成的偏序链与实施军事欺骗机会之间建立对应关系,再将此关系推广到基本概率矩阵,即是否存在实施军事欺骗的机会将由基本概率矩阵元素构成的偏序链决定.对理论成果的初步应用表明:通过分析由战场情报信息构成的基本概率矩阵的偏序链,可以科学地运用军事欺骗和反军事欺骗战法.     

一类具有标准发生率的SI型传染病模型的全局稳定性

研究如下一类具有标准发生率的SI型传染病模型{ds/dt=rS（1-（S＋I）/K-β SI/（S＋I）, dI/dt=βSI/（S＋I）-dI。应用微分方程定性理论，给出了该系统地方病平衡点、无病平衡点和总人口消亡平衡点的全局渐近稳定的充分条件。     

高功率密度柴油机智能化冷却系统控制策略

简要分析了未来坦克装甲车辆柴油机智能化控制冷却系统的必要性和可行性,提出了智能化冷却系统设计方案,阐述了其组成及工作原理,重点对智能化冷却系统控制策略进行了研究。针对某型柴油机,通过对其散热需求分析,提出了基于发动机工况的开环控制策略,同时,结合以发动机出口冷却水温度为控制目标提出了基于PID算法的闭环反馈控制策略。应用该策略可保证发动机在不同的环境和工况下冷却强度适宜,降低冷却系统的功耗。     

Stability in a general oligopoly model

We analyze a general but parsimonious price competition model for an oligopoly in which each firm offers any number of products. The demand volumes are general piecewise affine functions of the full price vector, generated as the “regular” extension of a base set of affine functions. The model specifies a product assortment, along with their prices and demand volumes, in contrast to most commonly used demand models. We identify a fully best response operator which is monotonically increasing so that the market converges to a Nash equilibrium, when firms dynamically adjust their prices, as best responses to their competitors' prices, at least when starting in one of two price regions. Moreover, geometrically fast convergence to a common equilibrium can be guaranteed for an arbitrary starting point, under an additional condition for the price sensitivity matrix.