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Predicting Real-World Penny Auction Durations by Integrating Game Theory and Machine Learning
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Proposes ADAPT, a three-stage framework that combines sentence-transformer product embeddings, game-theoretic (EUT and prospect-theory) duration predictions with learned parameter inference (InferNet), and a Multi-Branch Mixture Density Network to predict penny auction duration distributions.
Problem
Predicting the distribution of auction durations (and hence bid counts and auctioneer revenue) in penny auctions, where pure game-theory models lack accuracy and pure ML models fail under domain shift across auction configurations.
Approach
Use game-theoretic model predictions as domain knowledge, learn model parameters for unseen configurations from product embeddings with an InferNet, and feed both embeddings and game-theoretic predictions into a multi-branch Weibull mixture density network that outputs duration distributions.
Key results
- On real testing data, ADAPT achieves the lowest average NLL of 6.344 versus 6.795 for GT1 and 6.858 for GT2 (Table 2).
- ADAPT achieves the lowest KL-divergence on real data (2.836 vs 3.254 for GT1).
- InferNet-inferred GT2 parameters give NLL 6.858 on real data vs 7.421 for SA-Unified and 7.492 for SA-Avg.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ADAPT instead of GT1 | Auction duration prediction · Real testing data | NLL: 6.795 -> 6.344 | Helped |
| Use ADAPT instead of GT1 | Auction duration prediction · Real testing data | KL-D: 3.254 -> 2.836 | Helped |
| Use InferNet rather than SA-Avg to infer GT2 parameters | GT2 · Synthetic testing data, out-of-sample configurations | NLL: 7.938 -> 5.947 | Helped |
| Use InferNet rather than SA-Avg to infer GT2 parameters | GT2 · Real testing data, out-of-sample configurations | NLL: 7.492 -> 6.858 | Helped |
| Add an MDN to refine GT1 predictions (ablation) | Auction duration prediction · Real testing data | NLL: 6.795 -> 6.626 | Helped |
| Add product embeddings to GT1+MDN (ablation) | Auction duration prediction · Real testing data | NLL: 6.626 -> 6.454 | Helped |
| Add GT2 predictions to GT1+MDN with product embeddings (ablation) | Auction duration prediction · Real testing data | NLL: 6.454 -> 6.344 | Helped |
| Add product embeddings to GT1+GT2+MDN (ablation) | Auction duration prediction · Real testing data | NLL: 6.416 -> 6.344 | Helped |
| Add product embeddings to GT1+MDN (ablation) | Auction duration prediction · Real testing data | KL-D: 2.928 -> 2.848 | Helped |
| Add GT2 predictions to GT1+MDN with product embeddings (ablation) | Auction duration prediction · Real testing data | KL-D: 2.848 -> 2.836 | Helped |
Surprising findings
- Game-theory-only models with more flexible utility (GT2, prospect theory) did not outperform the simpler EUT-based GT1 on real data.
Limitations
- Evaluated only on penny auctions, so generalization to other strategic environments is untested.
- Game-theory models rely on symmetric subgame perfect Nash equilibrium assumptions and fixed functional forms.
- KL-divergence evaluation is sensitive to data scarcity and was reported only on real data.
Experimental setup
Datasets: real penny auction data from Byers et al. 2010 and Augenblick 2016 synthetic penny auction data generated from game theory models
Benchmarks: real penny auction data (testing split) synthetic penny auction data
Metrics: negative log-likelihood KL-divergence
Baselines: GT1 GT2 GT3 GT1+MDN GT2+MDN EMB+MDN GT1+EMB+MDN GT2+EMB+MDN GT1+GT2+MDN SA-Avg SA-Unified
Builds on: Mixture Density Network Prospect Theory Expected Utility Theory Sentence-BERT
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