网络上分层寻优主体群体的动力学--II：稳态分析
Dynamics of a Stratified Population of Optimum Seeking Agents on a Network -- Part II: Steady State Analysis
摘要：
在我们工作的第二部分中，我们研究了在第一部分中介绍的三个动态SSD，NBRD和NRPM的人口稳定状态和社会效用。我们提供了充分条件的基础上，每个节点的最大支付密度参数的网络上存在一个唯一的纳什均衡。然后，我们利用正相关属性的动态减少流图，以提供一个上界的稳定状态的社会效用。最后，我们扩展了背后的想法的充分条件存在一个唯一的纳什均衡适当地划分图，以提供一个下界的稳定状态的社会效用。我们还说明了有趣的情况下，以及我们的结果使用模拟。
英文摘要：
In this second part of our work, we study the steady state of the population and the social utility for the three dynamics SSD, NBRD and NRPM; which were introduced in the first part. We provide sufficient conditions on the network based on a maximum payoff density parameter of each node under which there exists a unique Nash equilibrium. We then utilize positive correlation properties of the dynamics to reduce the flow graph in order to provide an upper bound on the steady state social utility. Finally we extend the idea behind the sufficient condition for the existence of a unique Nash equilibrium to partition the graph appropriately in order to provide a lower bound on the steady state social utility. We also illustrate interesting cases as well as our results using simulations.
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