Complexity of Auctions with Interdependence
Patrick Loiseau, Simon Mauras, Minrui Xu

TL;DR
This paper investigates the complexity of designing truthful auction mechanisms in interdependent valuation models, removing domain restrictions, and providing both algorithms and hardness results for value and cost optimization.
Contribution
It introduces a comprehensive analysis of the computational complexity of truthful mechanisms in general interdependent settings, including new algorithms and hardness proofs.
Findings
Identifies tractable cases reducing to classical combinatorial problems.
Provides efficient algorithms for certain restricted cases.
Proves NP-hardness and query complexity lower bounds for the general case.
Abstract
We study auction design in the celebrated interdependence model introduced by Milgrom and Weber [1982], where a mechanism designer allocates a good, maximizing the value of the agent who receives it, while inducing truthfulness using payments. In the lesser-studied procurement auctions, one allocates a chore, minimizing the cost incurred by the agent selected to perform it. Most of the past literature in theoretical computer science considers designing truthful mechanisms with constant approximation for the value setting, with restricted domains and monotone valuation functions. In this work, we study the general computational problems of optimizing the approximation ratio of truthful mechanism, for both value and cost, in the deterministic and randomized settings. Unlike most previous works, we remove the domain restriction and the monotonicity assumption imposed on value…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAuction Theory and Applications · Game Theory and Applications · Game Theory and Voting Systems
