Sequential Mechanisms with ex-post Participation Guarantees

TL;DR

This paper characterizes revenue-optimal dynamic selling mechanisms over multiple periods with ex-post participation guarantees, providing a method to compute optimal mechanisms and a simple mechanism achieving at least half of the optimal revenue.

Contribution

It introduces a characterization of optimal dynamic mechanisms with ex-post participation constraints and proposes a simple mechanism that guarantees at least half of the optimal revenue.

Findings

Optimal mechanisms can be computed via nested static mechanisms.

A simple dynamic mechanism achieves at least 50% of the optimal revenue.

The approach extends to multi-agent and infinite horizon settings.

Abstract

We provide a characterization of revenue-optimal dynamic mechanisms in settings where a monopolist sells k items over k periods to a buyer who realizes his value for item i in the beginning of period i. We require that the mechanism satisfies a strong individual rationality constraint, requiring that the stage utility of each agent be positive during each period. We show that the optimum mechanism can be computed by solving a nested sequence of static (single-period) mechanisms that optimize a tradeoff between the surplus of the allocation and the buyer's utility. We also provide a simple dynamic mechanism that obtains at least half of the optimal revenue. The mechanism either ignores history and posts the optimal monopoly price in each period, or allocates with a probability that is independent of the current report of the agent and is based only on previous reports. Our characterization extends to multi-agent auctions. We also formulate a discounted infinite horizon version of the problem, where we study the performance of "Markov mechanisms."