Bayesian models of group learning are studied in Economics since the 1970s and more recently in computational linguistics. The models from Economics postulate that agents maximize utility in their communication and actions. The Economics models do not explain the ``probability matching" phenomena that are observed in many experimental studies. To address these observations, Bayesian models that do not formally fit into the economic utility maximization framework were introduced. In these models individuals sample from their posteriors in communication. In this work we study the asymptotic behavior of such models on connected networks with repeated communication. Perhaps surprisingly, despite the fact that individual agents are not utility maximizers in the classical sense, we establish that the individuals ultimately agree and furthermore show that the limiting posterior is Bayes optimal.

翻译：经济学界自20世纪70年代起便开始研究群体学习的贝叶斯模型，近年计算语言学领域也对此展开探讨。经济学模型假定主体在交流与行动中追求效用最大化，但这类模型无法解释诸多实验研究中观察到的"概率匹配"现象。为解释这些现象，学者们引入了形式上不完全符合经济学效用最大化框架的贝叶斯模型——在这些模型中，个体在交流中会从其后验分布进行采样。本研究分析了此类模型在具有重复交流的连通网络上的渐近行为。出乎意料的是，尽管个体在经典意义上并非效用最大化者，但我们证明了个体最终会达成一致，并进一步表明其极限后验分布具有贝叶斯最优性。