Complexity of Auctions with Interdependence
This addresses fundamental computational barriers in auction theory for both researchers and practitioners, though it is largely incremental within theoretical computer science.
The paper tackles the computational complexity of designing truthful auctions for both value maximization and cost minimization in the interdependence model without domain restrictions or monotonicity assumptions. It provides efficient algorithms for tractable special cases while proving NP-hardness and query complexity lower bounds for the general case.
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 functions. We provide theoretical explanations for why some previously considered special cases are tractable, reducing them to classical combinatorial problems, and providing efficient algorithms and characterizations. We complement our positive results with hardness results for the general case, providing query complexity lower bounds, and proving the NP-Hardness of the general case.