Optimal Multi-Item Auctions with I.I.D. Values

2026-10-07

AI Summary

This study addresses the core challenge of [specific problem] by proposing [method name], a novel approach grounded in [key technique/theoretical framework]. By introducing an innovative [mechanism], the proposed method effectively overcomes the performance bottlenecks inherent in conventional approaches. Experimental results demonstrate that our method achieves a [value]% improvement over state-of-the-art baselines on [benchmark datasets/evaluation metrics], significantly enhancing the model's [generalization capability/robustness/efficiency]. The primary contribution of this work lies in the first deep integration of [Technique A] with [Technique B], establishing a new paradigm for [research field] that offers both theoretical guarantees and practical utility.

Abstract

We study revenue-maximizing multi-item auctions under dominant-strategy incentive compatibility (DSIC) and ex-post individual rationality. Buyers have additive valuations, and all item values are independent draws from a common finite distribution. For every two-point distribution and arbitrary numbers of buyers and items, we give an explicit deterministic mechanism that is optimal among all randomized mechanisms satisfying these requirements, together with a polynomial-time algorithm for computing the optimal expected revenue. For general finite-support distributions, computing the exact optimal revenue is $\#\mathrm P$-hard, both for a single buyer with an arbitrary number of items and for two items with an arbitrary number of buyers. For a single buyer, we also establish hardness of computing an optimal mechanism. Building on prior work, we also obtain exact and approximate algorithms under different parameter restrictions. Exact polynomial-time optimization is possible whenever any two of the buyer count, item count, and support size are fixed. When only the item count is fixed, a polynomial-time approximation scheme constructs a mechanism with expected revenue at least a $1-\varepsilon$ fraction of the optimum for every fixed $0<\varepsilon<1$. All these algorithms satisfy DSIC and ex-post individual rationality.

Problem

• Multi-Item Auctions
• Revenue Maximization
• Dominant-Strategy Incentive Compatibility
• Computational Complexity
• I.I.D. Values

Innovation

• Multi-item auctions
• Revenue maximization
• Dominant-strategy incentive compatibility
• #P-hardness
• Polynomial-time approximation scheme