A robust optimization approach to mechanism design

• Main Authors: LI, Jiangtao, WANG, Kexin
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2024
• Subjects: mechanism design; local uncertainty; interim belief; robust optimization; duality approach; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/2765; https://ink.library.smu.edu.sg/context/soe_research/article/3764/viewcontent/RobustBayesian.pdf
• Institution: Singapore Management University

We study the design of mechanisms when the mechanism designer faces local uncertainty about agents’ beliefs. Specifically, we consider a designer who does not know the exact beliefs of the agents but is confident that her estimate is within ϵ of the beliefs held by the agents (where ϵ reflects the degree of local uncertainty). Adopting the robust optimization approach, we design mechanisms that incentivize agents to truthfully report their payoff-relevant information regardless of their actual beliefs. For any fixed ϵ, we identify necessary and sufficient conditions under which requiring this sense of robustness is without loss of revenue for the designer. By analyzing the limiting case in which ϵ approaches 0, we provide two rationales for the widely studied Bayesian mechanism design framework.