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Learning Optimal Auctions with Correlated Value Distributions
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Proposes Conditional Auction Net (CAN), a strategy-proof learned single-item auction whose monotone min-max rank-score functions take all bids as input, enabling revenue maximization under correlated values with closed-form differentiable payments.
Problem
Designing revenue-maximizing, strictly strategy-proof (ex-post IC and IR) single-item auctions when bidder values are correlated, where neural approaches like RegretNet only approximately satisfy incentive compatibility and MyersonNet cannot exploit correlation.
Approach
Rank-score functions parameterized as monotone min-max networks, increasing in a bidder's own bid and non-increasing in others' bids (single-crossing), take all bids as inputs so that one bidder's bid can shift others' winning probabilities; closed-form critical-bid payments from piecewise-linear intersections make the revenue loss differentiable and enforce strategy-proofness by architecture.
Key results
- CAN nearly matches the LP-derived optimal allocation rule for 2-bidder auctions, while CANw/oA only reaches a suboptimal increasing allocation curve.
- CAN matches RegretNet's revenue across 2-20 bidders and outperforms MyersonNet, CANw/oA and second-price auction.
- Under increasing value correlation, CAN revenue improves by 8.4% versus 6.4% for CANw/oA and 4.3% for MyersonNet.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use CAN instead of MyersonNet to model correlated bids | Single-item auctions · Irregular value distributions | revenue | Helped |
| use CAN instead of CANw/oA, which removes the additional virtual bidder (ablation) | CAN · Three-bidder auctions with irregular distributions (µ close to 0.5) | revenue | Helped |
| remove the additional virtual bidder (ablation) | CAN · Two-bidder auctions | allocation-rule expressiveness | Hurt |
| remove the additional virtual bidder (ablation) | CAN · Single-item auctions with fewer item reservations | revenue | No clear effect |
| increase value correlation | CAN · Normal distributions with varying correlations | revenue: 8.4% | Helped |
| increase value correlation (ablation) | CANw/oA · Normal distributions with varying correlations | revenue: 6.4% | Helped |
| increase value correlation | MyersonNet · Normal distributions with varying correlations | revenue: 4.3% | Helped |
| train with fewer samples | CAN · Few-shot training | data efficiency | Helped |
Surprising findings
- MyersonNet's fixed reserve price cannot adapt to other bidders' bids, limiting revenue even though it is strategy-proof.
Limitations
- Single-crossing condition is sufficient but not necessary, so CAN cannot represent all strategy-proof mechanisms.
- Evaluated only on single-item auctions with synthetic value distributions.
Experimental setup
Datasets: synthetic irregular correlated value distributions (mixtures of multivariate normals)
Benchmarks: synthetic correlated value distributions (2-20 bidders)
Metrics: revenue expressiveness (allocation rule visualization) training time few-shot data efficiency
Baselines: SP auction (Vickrey) MyersonNet RegretNet CANw/oA Linear programming
Builds on: MyersonNet RegretNet Myerson auction Monotonic networks (Sill 1997) Papadimitriou and Pierrakos geometric characterization
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