网络上分层优化群体的动力学--第一部分：建模与收敛性分析
Dynamics of a Stratified Population of Optimum Seeking Agents on a Network -- Part I: Modeling and Convergence Analysis
摘要：
在这项工作中，我们认为人口组成的一个连续体的代理人，寻求最大化的支付函数通过移动网络。网络中的节点可以表示物理位置或抽象选择。人口是分层的，因此选择相同选择的代理人可能不会得到相同的回报。特别是，我们假设支付函数，模型收益递减，也就是说，代理人在“新”层的节点收到一个较小的回报相比，“旧”层。在这两部分工作的第一部分，我们在三个选择修正政策下模拟人口动态，每个政策都有不同的协调水平。没有协调，代理人是自私的，ii.每个节点中的代理之间的协调，以及iii.整个人口的协调。为了对自私代理的情况进行建模，我们将Smith动力学推广到我们的设置，其中我们有分层的人口和网络约束。为了模拟节点协调，我们允许一个节点中的人口比例，作为一个整体，采取“最佳对策”的人口在节点附近的状态。对于人口范围内的协调的情况下，我们探讨了一个动态的人口演变根据集中的梯度上升的社会效用，虽然受到网络的约束。在每一种情况下，我们表明，动态的存在性和唯一性的解决方案，也表明，从任何初始条件的解决方案渐近收敛到纳什均衡。
英文摘要：
In this work, we consider a population composed of a continuum of agents that seek to maximize a payoff function by moving on a network. The nodes in the network may represent physical locations or abstract choices. The population is stratified and hence agents opting for the same choice may not get the same payoff. In particular, we assume payoff functions that model diminishing returns, that is, agents in "newer" strata of a node receive a smaller payoff compared to "older" strata. In this first part of two-part work, we model the population dynamics under three choice revision policies, each having varying levels of coordination -- i. no coordination and the agents are selfish, ii. coordination among agents in each node and iii. coordination across the entire population. To model the case with selfish agents, we generalize the Smith dynamics to our setting, where we have a stratified population and network constraints. To model nodal coordination, we allow the fraction of population in a node, as a whole, to take the `best response' to the state of the population in the node's neighborhood. For the case of population-wide coordination, we explore a dynamics where the population evolves according to centralized gradient ascent of the social utility, though constrained by the network. In each case, we show that the dynamics has existence and uniqueness of solutions and also show that the solutions from any initial condition asymptotically converge to the set of Nash equilibria.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
