Optimal Auctions with Restricted Allocations

TL;DR

This paper develops a duality framework for designing optimal auctions with restrictions on allocations, allowing for deterministic mechanisms and modeling non-additive valuations, and provides new characterizations and certifiable solutions.

Contribution

It extends duality results to restricted allocation settings, enabling certification of optimal mechanisms and broadening applicability beyond previous frameworks.

Findings

Proves a strong duality result for restricted auction mechanisms.

Provides a new characterization of feasible allocation sets.

Certifies optimal mechanisms in four novel settings.

Abstract

We study the problem of designing optimal auctions under restrictions on the set of permissible allocations. In addition to allowing us to restrict to deterministic mechanisms, we can also indirectly model non-additive valuations. We prove a strong duality result, extending a result due to Daskalakis et al. [2015], that guarantees the existence of a certificate of optimality for optimal restricted mechanisms. As a corollary of our result, we provide a new characterization of the set of allocations that the optimal mechanism may actually use. To illustrate our result we find and certify optimal mechanisms for four settings where previous frameworks do not apply, and provide new economic intuition about some of the tools that have previously been used to find optimal mechanisms.