Extending Myerson's Optimal Auctions to Correlated Bidders via Neural Network Interpolation

Mingyu Guo, Jiayuan Liu, Vincent Conitzer

Keywords: mechanism design, optimal auction, revenue maximization, virtual valuation

TL;DR: Myerson's landmark results on optimal auctions apply only to independent bidders. We extend Myerson's approach to correlated bidders via neural network interpolation and verification.

Abstract:

We aim to design revenue-maximizing single-item auctions that are deterministic, strategy-proof and ex post individually rational. Myerson's seminal work on optimal auction design solved this problem for independent bidders. Myerson introduced the novel concept of virtual valuation and showed that revenue maximization is equivalent to virtual valuation maximization. Coincidentally, by greedily allocating the item to the bidder with the highest (ironed) virtual valuation, the resulting allocation is guaranteed to be monotone -- a necessary and sufficient condition for strategy-proofness.

For correlated bidders, Myerson's greedy allocation no longer guarantees monotonicity/strategy-proofness. We propose a simple yet empirically effective approach for designing near-optimal auctions for correlated bidders. We train a neural network to interpolate the greedy allocation, while enforcing that the interpolation must be verifiably monotone.

Empirically, our method consistently achieves near-optimal revenue across a wide range of distributions, including adversarially generated cases. Compared to existing baselines, our approach shows substantial improvement, often reducing the gap to the (unattainable) greedy upper bound by an order of magnitude.

Furthermore, we demonstrate the generality of our approach by extending it to multi-unit auctions with unit demand, where we achieve similarly strong performance. Additionally, our verification techniques can be integrated into the RegretNet framework to design fully strategy-proof auctions.

Primary Area: other topics in machine learning (i.e., none of the above)

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Submission Number: 7898