A team from the Technical University of Munich (TUM) has succeeded in understanding complicated markets and their equilibrium methods using a new machine learning technique. Such analysis has thus far been limited to very simple auction marketplaces. The new numerical method opens up new avenues for economic theory and novel applications, such as wireless frequency auctions.

Game theory is a branch of mathematics that provides tools for describing the behavior of actors in strategic interactions. An important subfield of game theory is auction theory, which is used in economic theory to model markets. Several Nobel Prizes in Economic Sciences have been awarded in this area. Most recently to Robert Wilson and Paul Milgrom in 2020. The following principle controls auctions: Several parties interested in purchasing items submit bids. Parties can use a strategic strategy, such as bidding less than they are willing to spend to maximize profits. They must, however, be prepared for other parties to behave strategically as well.

Equilibrium points for complex auctions calculated for the first time

An essential concept for describing strategic behavior in auctions is the Bayes Nash equilibrium. This is the situation in which none of the parties could improve their expected utility by changing their strategy. Precise equilibrium strategies exist only for simple auctions, for example, when the parties are bidding on only one good.

“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,”

Prof. Bichler – Professor of Decision Sciences and Systems at TU Munich

Neural networks try to outbid each other

The new method, known as neural pseudo gradient ascent (NPGA), is based on many neural networks submitting competing bids and modifying their tactics after each round of bidding. They eventually arrive at a Bayes Nash equilibrium without explicitly solving the related differential equations using conventional methods.

“We can verify theoretically that the outcomes of the NPGA approach reliably converge to the equilibrium strategy for typical auction models,” explains Martin Bichler. “We also demonstrated in experiments that our process produces incredibly near approximations to market equilibrium strategies.”

Potential applications in theory and practice

Since the 1990s, governments worldwide have sold wireless spectrum through auctions to raise money for energy and other needs. “Spectrum auctions are an exciting real-world example,” says Martin Bichler, who is the editor of a handbook on spectrum auction design and has also served as a consultant in such auctions. “NPGA can help to 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.”