# Endogenous Quality in Social Learning

## TL;DR

This paper models how a seller's reputation and quality investments evolve over time in a social learning environment with limited observability, revealing conditions that influence quality levels and learning speed.

## Contribution

It introduces a dynamic reputation model with endogenous quality, characterizes equilibrium behaviors, and analyzes how information precision and disclosure affect investment and welfare.

## Key findings

- Quality is highest at intermediate reputation beliefs.
- Higher private signal precision can reduce investment and quality.
- Public disclosure expands investment regions and accelerates learning.

## Abstract

We study dynamic reputation in a social-learning environment where only purchase decisions are observable. A long-lived seller posts a fixed price and chooses costly product quality in each period before interacting with short-lived buyers who observe past purchases but not past consumption outcomes, and receive private signals about current quality. We embed this environment in a standard type-based reputation model with a small probability of a commitment type and characterize Markov equilibria. The belief space partitions into pessimistic and optimistic cascades and an interior learning region. In cascades the seller never invests in quality, while in the learning region equilibrium investment is inverse-U in reputation: quality is highest at intermediate beliefs and lowest at the extremes. This produces early-resolution and double-hump patterns for the evolution of beliefs and quality. When quality is endogenous, higher private signal precision can shrink the effective investment region and reduce equilibrium quality. Allowing flexible pricing or public disclosure of outcomes expands the region in which the seller invests, accelerates learning, and raises welfare.