Allocating Positional Goods: A Mechanism Design Approach

TL;DR

This paper uses mechanism design to analyze optimal allocation of positional goods considering externalities, showing how to maximize revenue and consumer surplus through various allocation strategies.

Contribution

It introduces a novel mechanism-design framework for allocating positional goods with externalities, including conditions for revenue maximization and participation effects.

Findings

Feasible allocations characterized by a majorization condition

Revenue-maximizing mechanisms may exclude some buyers

Offering more levels of goods affects consumer surplus depending on failure rates

Abstract

I study the optimal allocation of positional goods in the presence of externalities arising from consumers' concerns about relative consumption. Applications include luxury goods, priority services, education, and organizational hierarchies. Using a mechanism-design approach, I characterize the set of feasible allocations through a majorization condition. The revenue-maximizing mechanism possibly excludes some buyers and fully separates participants under Myerson's regularity condition. The seller can guarantee at least half the maximum revenue by offering a single good. Without exclusion, offering more levels of goods decreases (increases) consumer surplus under increasing (decreasing) failure rates. Higher participation raises consumer surplus under increasing failure rates.