Distributionally Robust Optimal Allocation with Costly Verification

• 成果类型: Article; Early Access
• 署名作者: Bayrak, Halil Ibrahim; Kocyigit, Cagil; Kuhn, Daniel; Pinar, Mustafa Celebi
• 署名单位: Ihsan Dogramaci Bilkent University; University of Luxembourg; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.0662
• 发表日期: 2025
• 关键词: Optimization

摘要

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 supportonly 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.