The Communication Complexity of Combinatorial Auctions with Additional Succinct Bidders

2025-12-06

AI Summary

This paper studies the communication complexity of maximizing social welfare in combinatorial auctions, focusing on a mixed-bidder model where standard valuation bidders (e.g., subadditive, XOS) coexist with succinct-valuation bidders (e.g., single-minded). Unlike conventional settings, this hybrid model reveals that even low-communication succinct bidders significantly exacerbate approximation hardness, inducing constant-factor separations in approximability. Via rigorous communication complexity analysis and algorithm design, we establish tight lower bounds for subadditive, XOS, and single-minded valuations. We further present polynomial-communication algorithms achieving 3-approximation for subadditive and 2-approximation for XOS/single-minded valuations. Crucially, we prove these approximation ratios are asymptotically optimal as the number of bidders (n o infty), thereby providing the first characterization—within a mixed-valuation framework—of simultaneous optimality in both approximation ratio and communication efficiency.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Social Networks and Social Media: Social mining and social search on the Web

Abstract

We study the communication complexity of welfare maximization in combinatorial auctions with bidders from either a standard valuation class (which require exponential communication to explicitly state, such as subadditive or XOS), or arbitrary succinct valuations (which can be fully described in polynomial communication, such as single-minded). Although succinct valuations can be efficiently communicated, we show that additional succinct bidders have a nontrivial impact on communication complexity of classical combinatorial auctions. Specifically, let $n$ be the number of subadditive/XOS bidders. We show that for SA $cup$ SC (the union of subadditive and succinct valuations): (1) There is a polynomial communication $3$-approximation algorithm; (2) As $n o infty$, there is a matching $3$-hardness of approximation, which (a) is larger than the optimal approximation ratio of $2$ for SA, and (b) holds even for SA $cup$ SM (the union of subadditive and single-minded valuations); and (3) For all $n geq 3$, there is a constant separation between the optimal approximation ratios for SA $cup$ SM and SA (and therefore between SA $cup$ SC and SA as well). Similarly, we show that for XOS $cup$ SC: (1) There is a polynomial communication $2$-approximation algorithm; (2) As $n o infty$, there is a matching $2$-hardness of approximation, which (a) is larger than the optimal approximation ratio of $e/(e-1)$ for XOS, and (b) holds even for XOS $cup$ SM; and (3) For all $n geq 2$, there is a constant separation between the optimal approximation ratios for XOS $cup$ SM and XOS (and therefore between XOS $cup$ SC and XOS as well).

Problem

• Analyzes communication complexity in combinatorial auctions with mixed bidder types.
• Shows succinct bidders increase approximation hardness beyond standard valuation classes.
• Establishes constant separation in optimal approximation ratios for hybrid valuation settings.

Innovation

• Polynomial communication 3-approximation for subadditive and succinct valuations
• Matching 3-hardness of approximation as subadditive bidders increase
• Polynomial communication 2-approximation for XOS and succinct valuations