Revenue-Optimal Deterministic Auctions for Multiple Buyers with Ordinal Preferences over Fixed-price Items

TL;DR

This paper explores revenue-maximizing deterministic auctions for multiple buyers with ordinal preferences over fixed-price items, revealing tractable solutions under Markov Chain ranking models and complexities beyond them.

Contribution

It introduces a Bayesian mechanism design model with fixed prices and ordinal preferences, showing optimal mechanisms are tractable under Markov Chain models and highlighting challenges outside this setting.

Findings

Optimal mechanisms are virtual welfare maximizers under Markov Chain rankings.

Computational tractability is achieved for independent Markov Chain ranking distributions.

Optimal mechanisms may not be virtual welfare maximizers outside Markov Chain models.

Abstract

In this paper, we introduce a Bayesian revenue-maximizing mechanism design model where the items have fixed, exogenously-given prices. Buyers are unit-demand and have an ordinal ranking over purchasing either one of these items at its given price, or purchasing nothing. This model arises naturally from the assortment optimization problem, in that the single-buyer optimization problem over deterministic mechanisms reduces to deciding on an assortment of items to "show". We study its multi-buyer generalization in the simplest setting of single-winner auctions, or more broadly, any service-constrained environment. Our main result is that if the buyer rankings are drawn independently from Markov Chain ranking models, then the optimal mechanism is computationally tractable, and structurally a virtual welfare maximizer. We also show that for ranking distributions not induced by Markov Chains, the optimal mechanism may not be a virtual welfare maximizer.