Bayesian Learning without Recall

TL;DR

This paper introduces a Bayesian without Recall model for social learning, simplifying belief updates in networks where agents lack memory of past observations, and explores its implications for learning and consensus.

Contribution

It proposes a tractable Bayesian inference framework without recall, bridging rational inference and non-Bayesian update rules in social networks.

Findings

The model facilitates analysis of belief convergence and consensus.

It highlights limitations of Bayesian updating with memory in social learning.

The framework connects rational inference to observed non-Bayesian behaviors.

Abstract

We analyze a model of learning and belief formation in networks in which agents follow Bayes rule yet they do not recall their history of past observations and cannot reason about how other agents' beliefs are formed. They do so by making rational inferences about their observations which include a sequence of independent and identically distributed private signals as well as the actions of their neighboring agents at each time. Successive applications of Bayes rule to the entire history of past observations lead to forebodingly complex inferences: due to lack of knowledge about the global network structure, and unavailability of private observations, as well as third party interactions preceding every decision. Such difficulties make Bayesian updating of beliefs an implausible mechanism for social learning. To address these complexities, we consider a Bayesian without Recall model of inference. On the one hand, this model provides a tractable framework for analyzing the behavior of rational agents in social networks. On the other hand, this model also provides a behavioral foundation for the variety of non-Bayesian update rules in the literature. We present the implications of various choices for the structure of the action space and utility functions for such agents and investigate the properties of learning, convergence, and consensus in special cases.