Distribution dependent stochastic differential equations

Due to their intrinsic link with nonlinear Fokker-Planck equations and many other applications, distribution dependent stochastic differential equations (DDSDEs) have been intensively investigated. In this paper, we summarize some recent progresses in the study of DDSDEs, which include the correspondence of weak solutions and nonlinear Fokker-Planck equations, the well-posedness, regularity estimates, exponential ergodicity, long time large deviations, and comparison theorems.     

Differentiable spaces that are subcartesian

We show that the differential structure of the orbit space of a proper action of a Lie group on a smooth manifold is weakly reflexive. This implies that the orbit space is a differentiable space in the sense of Smith, which ensures that the orbit space has an exterior algebra of differential forms, that satisfies Smith’s version of de Rham’s theorem. Because the orbit space is a locally closed subcartesian space, it has vector fields and their flows.     

Collective Strategy Condensation: When Envy Splits Societies

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.     

Linearizability of planar polynomial Hamiltonian systems

Isochronicity and linearizability of two-dimensional polynomial Hamiltonian systems are revisited and new results are presented. We give a new computational procedure to obtain the necessary and sufficient conditions for the linearization of a polynomial system. Using computer algebra systems we provide necessary and sufficient conditions for linearizability of Hamiltonian systems with homogeneous non-linearities of degrees 5, 6 and 7. We also present some sufficient conditions for systems with nonhomogeneous nonlinearities of degrees two, three and five.     

不同补贴对象下闭环供应链信息共享价值研究

在一个制造商和一个零售商组成的二级闭环供应链中,为研究政府补贴下供应链需求信息共享对决策的影响及共享价值,针对两种补贴对象,构建并求解无信息共享和信息共享博弈模型,并进行仿真验证.研究表明:1)两种补贴对象下,制造商均能从信息共享中获益,零售商仅在绿色成本和回收成本较低时才会从信息共享中获益;绿色成本和回收成本稍高时,设计基于谈判势力的信息补偿机制能有效促进零售商共享信息.2)产品绿色度和回收率随预测需求量的提高而提高,批发价和零售价仅在回收成本较低时,才会随预测需求量的提高而提高.3)在仅补贴一方情况下,当补贴对象为低补贴一方时,两个主体所获的信息共享价值大;若对两者的补贴均较低,两个主体均希望补贴对象为零售商;若对两者的补贴均较高,零售商不愿共享需求信息.     

政府监管下的医院医疗信息分享演化博弈分析

在分析政府监管下医院间医疗信息分享特征的基础上,结合我国当前正在推行的医联体医院间信息分享运作模式,引入梅特卡夫定律并考虑患者评价的影响,分析了监管部门与医院各自的利益组成,建立了监管部门与医院两者之间的演化博弈模型,并采用复制动态方程研究了不同情形下医院间信息分享的演化博弈轨迹。研究表明,政府通过监管并建立激励惩罚机制等引导措施对医院最终达到的演化稳定态具有极大影响;降低医院主体信息分享的风险成本、规范提高医院分享信息的质量、引导患者增强对医院信息分享的关注、制定有吸引力和威慑力的奖惩政策,是促进医院医疗信息分享的关键。研究结果可为政府监管部门预测医院间的信息分享趋势和制定精准化政策以促进分享提供参考。