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Coordination problems on networks revisited: statics and dynamics
arXiv - CS - Computer Science and Game Theory Pub Date : 2021-06-04 , DOI: arxiv-2106.02548
Luca Dall'Asta

Simple binary-state coordination models are widely used to study collective socio-economic phenomena such as the spread of innovations or the adoption of products on social networks. The common trait of these systems is the occurrence of large-scale coordination events taking place abruptly, in the form of a cascade process, as a consequence of small perturbations of an apparently stable state. The conditions for the occurrence of cascade instabilities have been largely analysed in the literature, however for the same coordination models no sufficient attention was given to the relation between structural properties of (Nash) equilibria and possible outcomes of dynamical equilibrium selection. Using methods from the statistical physics of disordered systems, the present work investigates both analytically and numerically, the statistical properties of such Nash equilibria on networks, focusing mostly on random graphs. We provide an accurate description of these properties, which is then exploited to shed light on the mechanisms behind the onset of coordination/miscoordination on large networks. This is done studying the most common processes of dynamical equilibrium selection, such as best response, bounded-rational dynamics and learning processes. In particular, we show that well beyond the instability region, full coordination is still globally stochastically stable, however equilibrium selection processes with low stochasticity (e.g. best response) or strong memory effects (e.g. reinforcement learning) can be prevented from achieving full coordination by being trapped into a large (exponentially in number of agents) set of locally stable Nash equilibria at low/medium coordination (inefficient equilibria). These results should be useful to allow a better understanding of general coordination problems on complex networks.

中文翻译:

重新审视网络上的协调问题:静态和动态

简单的二元状态协调模型被广泛用于研究集体社会经济现象,例如创新的传播或产品在社交网络上的采用。这些系统的共同特征是大规模协调事件以级联过程的形式突然发生,这是明显稳定状态的小扰动的结果。文献中已经大量分析了级联不稳定性发生的条件,但是对于相同的协调模型,没有对(纳什)平衡的结构特性与动态平衡选择的可能结果之间的关系给予足够的关注。使用来自无序系统的统计物理学的方法,目前的工作从分析和数值上进行研究,网络上这种纳什均衡的统计特性,主要集中在随机图上。我们提供了对这些属性的准确描述,然后利用这些描述来阐明大型网络上协调/错误协调发生背后的机制。这是通过研究最常见的动态均衡选择过程完成的,例如最佳响应、有限理性动态和学习过程。特别是,我们表明,远远超出不稳定区域,完全协调仍然是全局随机稳定的,但是具有低随机性(例如最佳响应)或强记忆效应(例如 强化学习)可以通过被困在低/中协调(低效均衡)下的大量(代理数量呈指数级)局部稳定纳什均衡中而无法实现完全协调。这些结果应该有助于更好地理解复杂网络上的一般协调问题。
更新日期:2021-06-07
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