Auction theory is an essential subfield of game theory. It is mainly used in economic theory to model markets.
Auctions depend on the accompanying rule: Bids are submitted by several parties looking to buy products. The parties can take an essential strategy, for instance, by bidding less than they will spend to augment their benefits. However, they should be ready for other parties to act strategically, as well.
The Bayes Nash equilibrium is an essential concept for describing strategic behavior in auctions.
In simple terms, this is when none of the parties could improve their expected utility by changing their strategy – a sort of optimal line. An equilibrium of this kind can be modeled as a system of differential equations that cannot be solved precisely in more complex markets. Precise equilibrium strategies exist only for simple auctions, for example, when the parties are bidding on only one good.
Scientists at the Technical University of Munich (TUM) used a machine-learning algorithm to analyze complex markets and equilibrium strategies. This new method opens up new possibilities for economic theory and new applications, like wireless spectrum auctions.
Martin Bichler, Professor of Decision Sciences and Systems at TUM said: “Machine learning is not yet widely used in auction theory. Using neural networks, we were able to compute equilibrium strategies for complex auction models that were previously unsolvable.”
“For common auction models, we can prove mathematically that the results of the NPGA method reliably converge to the equilibrium strategy. We also showed in experiments that our process delivers extremely close approximations to equilibrium strategies for markets.”
“The new algorithm will help economists to analyze more complex markets and their equilibria. But real-world applications are also conceivable: Since the mid-1990s, governments worldwide have sold wireless spectrum through auctions. The Nobel laureates Robert Wilson and Paul Milgrom have developed auction formats for this purpose.”
“Spectrum auctions are an exciting real-world example. NPGA can help identify strategic issues in advance that could lead to undesirable results – for example, a high likelihood of bidding strategies resulting in spectrum licenses being purchased by inefficient bidders. In this case, the organizers could opt for a different auction mechanism. And conversely, the algorithm could also support bidders in developing their bidding strategies.”
The source code is available here.
- Bichler, M., Fichtl, M., Heidekrüger, S, Kohring, N., Sutterer, P. Learning equilibria in symmetric auction games using artificial neural networks. Nature Machine Intelligence (2021). DOI: 10.1038/s42256-021-00365-4