# An n-to-1 Bidder Reduction for Multi-item Auctions and its Applications

arXiv: https://arxiv.org/abs/1406.3278 · HTML: https://mlsanity.com/paper/1406.3278/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2014.

## Built on by (most cited first, 7 of 7)

- [Differentiable Economics for Randomized Affine Maximizer Auctions](https://mlsanity.com/paper/2202.02872/) (2022)
- [A Context-Integrated Transformer-Based Neural Network for Auction Design](https://mlsanity.com/paper/2201.12489/) (2022)
- [Recommender Systems meet Mechanism Design](https://mlsanity.com/paper/2110.12558/) (2021)
- [Learning Optimal Posted Prices for a Unit-Demand Buyer](https://mlsanity.com/paper/2506.02284/) (2025)
- [A Robust Multi-Item Auction Design with Statistical Learning](https://mlsanity.com/paper/2302.00941/) (2023)
- [Refined Mechanism Design for Approximately Structured Priors via Active Regression](https://mlsanity.com/paper/2310.07874/) (2023)
- [Regularized Proportional Fairness Mechanism for Resource Allocation Without Money](https://mlsanity.com/paper/2501.01111/) (2025)

## Abstract (arXiv)

In this paper, we introduce a novel approach for reducing the k-item n-bidder auction with additive valuation to k-item 1-bidder auctions. This approach, called the Best-Guess reduction, can be applied to address several central questions in optimal revenue auction theory such as the power of randomization, and Bayesian versus dominant-strategy implementations. First, when the items have independent valuation distributions, we present a deterministic mechanism called it Deterministic Best-Guess that yields at least a constant fraction of the optimal revenue by any randomized mechanism. Second, if all the nk valuation random variables are independent, the optimal revenue achievable in it dominant strategy incentive compatibility (DSIC) is shown to be at least a constant fraction of that achievable in it Bayesian incentive compatibility (BIC). Third, when all the nk values are identically distributed according to a common one-dimensional distribution F, the optimal revenue is shown to be expressible in the closed form Theta(k(r+int0mr (1-F(x)n) ud x)) where r= supx≥ 0 , x(1 - F(x)n) and m=lceil k/nrceil; this revenue is achievable by a simple mechanism called 2nd-Price Bundling. All our results apply to arbitrary distributions, regular or irregular.