论文标题
网络上最佳寻求代理的分层人群的动力学 - 第一部分：建模和收敛分析
Dynamics of a Stratified Population of Optimum Seeking Agents on a Network -- Part I: Modeling and Convergence Analysis
论文作者
论文摘要
在这项工作中，我们考虑了一个由连续代理组成的人群，这些代理商试图通过在网络上移动来最大化回报功能。网络中的节点可以代表物理位置或抽象选择。人口分层，因此选择同一选择的代理商可能不会获得相同的回报。特别是，我们假设模型减少回报的回报功能，即与“较旧”地层相比，节点“较新”层中的代理会获得更小的回报。在两部分工作的第一部分中，我们在三个选择修订策略下对种群动态进行建模，每个人的协调水平都不同。没有协调，代理人是自私的，ii。每个节点和III中的代理之间的协调。整个人口的协调。为了用自私的代理建模案例，我们将史密斯动力学推广到我们的设置，在那里我们具有分层的人群和网络约束。为了对节点的协调进行建模，我们允许整个节点中的人口比例的一部分，以对节点社区中人口状态的“最佳响应”采取“最佳响应”。对于在人口范围内的协调情况下，我们探索了一种动态，尽管受到网络的限制，但人口根据社会效用的集中梯度演变而发展。在每种情况下，我们都表明动力学具有解决方案的存在和独特性，并且还表明，从任何初始条件的求解方案均不融合到NASH均衡的集合。
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.
