Distributionally Robust Optimal Allocation with Costly Verification

TL;DR

This paper develops a robust mechanism design framework for allocating a single good to agents with private types, considering costly verification and ambiguity in joint type distributions, resulting in explicit Pareto-robustly optimal mechanisms.

Contribution

It introduces explicit favored-agent mechanisms that are robust against distributional ambiguity in agents' types, extending prior models that assumed known independent distributions.

Findings

Constructed explicit Pareto-robustly optimal mechanisms.

Analyzed support-only and Markov ambiguity sets.

Mechanisms perform well under worst-case distributional assumptions.

Abstract

We consider the mechanism design problem of a principal allocating a single good to one of several agents without monetary transfers. Each agent desires the good and uses it to create value for the principal. We designate this value as the agent's private type. Even though the principal does not know the agents' types, she can verify them at a cost. The allocation of the good thus depends on the agents' self-declared types and the results of any verification performed, and the principal's payoff matches her value of the allocation minus the costs of verification. It is known that if the agents' types are independent, then a favored-agent mechanism maximizes her expected payoff. However, this result relies on the unrealistic assumptions that the agents' types follow known independent probability distributions. In contrast, we assume here that the agents' types are governed by an ambiguous joint probability distribution belonging to a commonly known ambiguity set and that the principal maximizes her worst-case expected payoff. We study support-only ambiguity sets, which contain all distributions supported on a rectangle, Markov ambiguity sets, which contain all distributions in a support-only ambiguity set satisfying some first-order moment bounds, and Markov ambiguity sets with independent types, which contain all distributions in a Markov ambiguity set under which the agents' types are mutually independent. In all cases we construct explicit favored-agent mechanisms that are not only optimal but also Pareto-robustly optimal.