Dynamic Pricing with Limited Commitment

TL;DR

This paper analyzes a monopolist's dynamic pricing problem with limited commitment, showing that equilibrium revenue cannot exceed that of pre-committed pricing, regardless of consumer information persistence.

Contribution

It demonstrates that in a dynamic setting with evolving private information, limited commitment restricts revenue to pre-committed levels, even with persistent consumer information.

Findings

Equilibrium revenue is capped at pre-committed pricing levels.

Persistence of consumer information does not increase seller revenue.

D1 refinement ensures no revenue gain from dynamic pricing strategies.

Abstract

A monopolist wants to sell one item per period to a consumer with evolving and persistent private information. The seller sets a price each period depending on the history so far, but cannot commit to future prices. We show that, regardless of the degree of persistence, any equilibrium under a D1-style refinement gives the seller revenue no higher than what she would get from posting all prices in advance.