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Auctionformer: A Unified Deep Learning Algorithm for Solving Equilibrium Strategies in Auction Games

ICML 2024 · Architectures and efficiency › Pruning and efficient tuning · approach: Low-rank compression and merging

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Proposes Auctionformer, a BERT-based transformer that tokenizes diverse single-item auctions and solves approximate Bayes-Nash equilibrium bidding strategies in one forward pass, trained with a Nash-error loss and adapted via a few-shot preservation-loss scheme.

Problem

Solving approximate Bayesian Nash equilibria across many auction mechanisms and bidder configurations, where existing no-regret, MARL, and numerical solvers are mechanism-specific and resource-intensive.

Approach

Tokenize mechanisms and discretized bidder value distributions into a standard token sequence fed to a pretrained Transformer with an attention-based value-query decoder, and train it with the Nash (max exploitability) error as loss instead of MSE/CE, so no equilibrium labels are needed; few-shot adaptation uses Nash loss plus a preservation loss on prior data.

Key results

• Auctionformer achieves max exploitability around 1e-4 across FP, SP, FP+Ent, SP+Ent for 2-10 bidders, about 10^3 times lower than random strategies (1.59e-1).
• Few-shot Nash+preservation loss reduces N=15 error from 5.67e-02 (pretrained) to 2.94e-03 while keeping N<=10 error at 4.01e-04.
• Auctionformer's runtime stays roughly constant with bidder count, whereas MWU's grows sharply from 2 to 10 bidders.

Measured effects reported in the paper

Surprising findings

• Larger pretrained language models converge in fewer training epochs (LLaMA2-7B needed 5 epochs vs 81 for BERT-small).

Limitations

• Evaluated only on single-item auctions with discretized value space (H=20) and bids in [0,1]-projected space.
• Mechanism coverage limited to first-price and second-price auctions with optional entry fees.
• Few-shot results on out-of-domain cases still show higher error (e.g., 2.94e-03 at N=15) than in-domain.

Experimental setup

Datasets: synthetic auction games with Uniform and Gaussian value distributions

Benchmarks: synthetic auction games (FP, SP, FP+Ent, SP+Ent)

Metrics: Nash error (max exploitability) L2 distance to theoretical solution runtime

Baselines: MWU MLPNet NPGA SODA SM backward-shooting

Builds on: BERT RegretNet Nikaido-Isoda function DreamBooth

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