We study convergence rates of random-order best-response dynamics in games on networks with linear best responses and strategic substitutes. Combining formal analysis with numerical simulations we identify phenomena that lead to slow convergence. One of the key such phenomena is convergence to stable strategy profiles in parts of the network neighboring sets of nodes which remain inactive until the dynamics is close to converging and then switch to activity, initiating convergence to profiles with a new set of active agents and possibly leading to another iteration of such behavior. We identify structural properties of graphs which make such phenomena more likely. These properties go beyond the spectrum of a graph, which we demonstrate analyzing convergence rates on co-spectral mates.

翻译：本研究探讨具有线性最优响应与策略替代特性的网络博弈中随机顺序最优响应动态的收敛速率。通过形式化分析与数值模拟相结合，我们识别了导致收敛缓慢的关键现象。其中核心现象表现为：动态过程会收敛至网络的局部稳定策略剖面，这些区域邻近的节点集在动态过程接近收敛前保持非活跃状态，随后突然转为活跃状态，从而引发向新活跃代理集合的收敛过程，并可能导致此类行为的多次迭代。我们进一步识别了使此类现象更易发生的图结构特性。这些特性超越了图谱分析范畴，我们通过分析共谱图对的收敛速率对此进行了验证。