On the sufficiency of unidirectional incentive compatibility in auctions

2026-06-01

AI Summary

This study addresses revenue maximization in auction mechanism design when bidders are constrained to underreport their valuations unilaterally. The work proposes that enforcing only one-sided incentive compatibility—sufficient to prevent underbidding—is adequate to achieve the same maximal revenue as full incentive compatibility. By employing linear programming duality in a discrete valuation model, the authors theoretically establish the sufficiency of one-sided incentive compatibility for revenue optimality, thereby substantially simplifying the characterization of feasible allocation rules in multi-agent settings. This result uncovers a tractable pathway for mechanism design under specific bias constraints and offers rigorous theoretical support for practical auction systems where strategic misreporting is limited to downward deviations.

Abstract

We study optimal auction design when the direction of bidders' deviations is restricted. We show that the optimal revenue when bidders can only underbid their true values cannot exceed the optimal revenue when bidders may freely underbid or overbid. Thus, unidirectional incentive compatibility is sufficient for full incentive compatibility for revenue maximization. We prove this equivalence through linear programming duality in a discrete model, which makes it possible to analyze the feasibility of allocation rules in multi-agent environments.

Problem

• auction design
• incentive compatibility
• revenue maximization
• unidirectional deviation
• mechanism design

Innovation

• unidirectional incentive compatibility
• optimal auction design
• linear programming duality
• revenue maximization
• allocation rules