Optimal Auction Design for Flexible Consumers

TL;DR

This paper develops an optimal auction framework for allocating multiple goods to flexible consumers with nested flexibility sets, providing simplified allocation and payment rules that maximize revenue while ensuring incentive compatibility and individual rationality.

Contribution

It introduces a novel auction design for nested flexibility sets, characterizing optimal allocations and payments through thresholds, and simplifies complex incentive constraints.

Findings

Optimal auction characterized as an integer program.

Payment rules described by an integral equation.

Simplified threshold-based allocation and payment rules.

Abstract

We study the problem of designing revenue-maximizing auctions for allocating multiple goods to flexible consumers. In our model, each consumer is interested in a subset of goods known as its flexibility set and wants to consume one good from this set. A consumer's flexibility set and its utility from consuming a good from its flexibility set are its private information. We focus on the case of nested flexibility sets --- each consumer's flexibility set can be one of $k$ nested sets. We provide several examples where such nested flexibility sets may arise. We characterize the allocation rule for an incentive compatible, individually rational and revenue-maximizing auction as the solution to an integer program. The corresponding payment rule is described by an integral equation. We then leverage the nestedness of flexibility sets to simplify the optimal auction and provide a complete characterization of allocations and payments in terms of simple thresholds.