Sequential Naive Learning

TL;DR

This paper studies how boundedly rational agents sequentially update their beliefs and actions based on aggregate statistics and signals, demonstrating conditions for asymptotic learning in binary state-action models.

Contribution

It introduces a model of sequential naive learning with aggregate-based priors, showing convergence to the true state under probability matching and extending to multiple states and actions.

Findings

Actions converge to the true state in probability under certain decision rules.

Discretized DeGroot rule leads to asymptotic learning in binary models.

Results extend to multiple states and actions.

Abstract

We analyze boundedly rational updating from aggregate statistics in a model with binary actions and binary states. Agents each take an irreversible action in sequence after observing the unordered set of previous actions. Each agent first forms her prior based on the aggregate statistic, then incorporates her signal with the prior based on Bayes rule, and finally applies a decision rule that assigns a (mixed) action to each belief. If priors are formed according to a discretized DeGroot rule, then actions converge to the state (in probability), i.e., \emph{asymptotic learning}, in any informative information structure if and only if the decision rule satisfies probability matching. This result generalizes to unspecified information settings where information structures differ across agents and agents know only the information structure generating their own signal. Also, the main result extends to the case of $n$ states and $n$ actions.