论文标题
社交攀岩和Amoroso分布
Social climbing and Amoroso distribution
论文作者
论文摘要
我们介绍了Boltzmann和Fokker（Planck Type）的一类一维线性动力学方程，描述了多机构社会的个人的动态，以寻求社会层次结构中的高地位。在Boltzmann级别上，代理商围绕普遍期望的目标状态的显微镜变化是在引入地位变化的主要标准的，这是基于Kahneman和Twersky的前景理论精神的合适价值功能。在放牧相互作用的渐近学中，玻尔兹曼型动力学方程的溶液密度显示出朝向fokker-planck型方程的溶液，具有扩散和漂移的可变系数，其特征在于值函数的数学特性。 Fokker预测的社会状况的统计分布的稳态 - Planck方程属于带有帕累托尾巴的Amoroso分布类别，这与\ Emph {Social Elite}的出现相对应。微观动力学相互作用的细节允许阐明表征所得平衡的各种参数的含义。然后，数值结果表明，即使在相互作用没有放牧的中间状态下，基本动力学方程的稳态也接近Amoroso分布。
We introduce a class of one-dimensional linear kinetic equations of Boltzmann and Fokker--Planck type, describing the dynamics of individuals of a multi-agent society questing for high status in the social hierarchy. At the Boltzmann level, the microscopic variation of the status of agents around a universal desired target, is built up introducing as main criterion for the change of status a suitable value function in the spirit of the prospect theory of Kahneman and Twersky. In the asymptotics of grazing interactions, the solution density of the Boltzmann type kinetic equation is shown to converge towards the solution of a Fokker--Planck type equation with variable coefficients of diffusion and drift, characterized by the mathematical properties of the value function. The steady states of the statistical distribution of the social status predicted by the Fokker--Planck equations belong to the class of Amoroso distributions with Pareto tails, which correspond to the emergence of a \emph{social elite}. The details of the microscopic kinetic interaction allow to clarify the meaning of the various parameters characterizing the resulting equilibrium. Numerical results then show that the steady state of the underlying kinetic equation is close to Amoroso distribution even in an intermediate regime in which interactions are not grazing.
