Screening with damages and ordeals

TL;DR

This paper compares damages and ordeals as screening tools in mechanism design, showing damages are generally dominated by ordeals unless agents' valuations are heterogeneous across multiple goods, where damages can be optimal.

Contribution

It characterizes when damages are optimal versus dominated, highlighting the role of valuation heterogeneity in multidimensional screening mechanisms.

Findings

Damages are Pareto-dominated when agents share valuations for one good.

Damages can be optimal with heterogeneous valuations across multiple goods.

Optimal mechanisms often use market-clearing ordeals under certain distributional conditions.

Abstract

A welfare-maximizing designer allocates two kinds of goods using two wasteful screening instruments: ordeals, which enter agents' utilities additively, and damages, which harm agents in proportion to their values for the goods. If agents have common valuations for one of the goods, damages always lead to Pareto-dominated mechanisms: any allocation using damages can be implemented with ordeals alone, while leaving higher rents to inframarginal types. However, damages can be optimal when agents' valuations for both goods are heterogeneous: with multidimensional types, the two devices differ in how they sort agents into the available options, and optimal sorting can sometimes require damages. I nevertheless identify distributional conditions under which damages are not optimal. In those cases, the optimal mechanism produces an efficient allocation by posting ``market-clearing'' ordeals for each good.