Deterministic Refund Mechanisms

TL;DR

This paper studies the design of optimal deterministic refund mechanisms in a single-item, single-buyer setting where the buyer's true value is revealed only after purchase, providing a characterization and algorithms for optimality.

Contribution

It introduces a novel framework for deterministic refund mechanisms, characterizes optimal mechanisms as virtual value maximizers, and develops efficient algorithms for their computation.

Findings

Optimal mechanisms are characterized as virtual value maximizers.

Efficient algorithms are developed for finding optimal and near-optimal mechanisms.

Bounds on menu size complexity are established.

Abstract

We consider a mechanism design setting with a single item and a single buyer who is uncertain about the value of the item. Both the buyer and the seller have a common model for the buyer's value, but the buyer discovers her true value only upon receiving the item. Mechanisms in this setting can be interpreted as randomized refund mechanisms, which allocate the item at some price and then offer a (partial and/or randomized) refund to the buyer in exchange for the item if the buyer is unsatisfied with her purchase. Motivated by their practical importance, we study the design of optimal deterministic mechanisms in this setting. We characterize optimal mechanisms as virtual value maximizers for both continuous and discrete type settings. We then use this characterization, along with bounds on the menu size complexity, to develop efficient algorithms for finding optimal and near-optimal deterministic mechanisms.