Complexity of Auctions with Interdependence

2026-03-19

AI Summary

This study addresses the design of approximately optimal incentive-compatible mechanisms that are computationally feasible under the Milgrom–Weber interdependent valuation model, encompassing both welfare-maximization (item allocation) and cost-minimization (task assignment) settings. Departing from conventional assumptions on monotonicity and domain restrictions of valuation functions, this work provides the first unified treatment of value and cost auctions within a general interdependent framework. By integrating mechanism design theory, computational complexity analysis, and query complexity models, it establishes connections between tractable instances and classical combinatorial optimization problems, yielding efficient algorithms and structural characterizations for these cases. Moreover, it proves that mechanism design in the general setting is NP-hard and derives corresponding lower bounds on query complexity.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

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 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.

Problem

• auction design
• interdependent valuations
• truthful mechanisms
• approximation ratio
• computational complexity

Innovation

• interdependent valuations
• truthful mechanism design
• approximation ratio optimization
• computational complexity
• procurement auctions