# Optimal mechanism for the sale of a durable good

## TL;DR

This paper demonstrates that in a durable good sale with a fully persistent binary valuation, posted prices can implement all equilibrium outcomes, confirming the seller's inability to do better than simple pricing due to Coase's conjecture.

## Contribution

It shows that posted prices suffice to implement all equilibrium outcomes in an infinite-horizon durable good sale with limited commitment, linking mechanism design and durable goods literature.

## Key findings

- Posted prices implement all equilibrium outcomes.
- Seller cannot outperform simple pricing, confirming Coase's conjecture.
- Analysis uses the revelation principle to connect information and mechanism design.

## Abstract

A buyer wishes to purchase a durable good from a seller who in each period chooses a mechanism under limited commitment. The buyer's valuation is binary and fully persistent. We show that posted prices implement all equilibrium outcomes of an infinite-horizon, mechanism selection game. Despite being able to choose mechanisms, the seller can do no better and no worse than if he chose prices in each period, so that he is subject to Coase's conjecture. Our analysis marries insights from information and mechanism design with those from the literature on durable goods. We do so by relying on the revelation principle in Doval and Skreta (2020).