Researchers at TUM Introduce A Machine Learning Method That can Learn Local Equilibria in Symmetric Auction Games Using Artificial Neural Networks

Computer scientists have been researching the prospect of applying game theory and (AI) artificial intelligence technologies to chess, the abstract strategic board game, and other games for several decades. Another practical application of game theory is in economics, where it is used to explain strategic market interactions and eventual outcomes.

Auction theory is one of the most frequent theoretical constructs used to apply game theory in economics. Auction theory is based on a game theory that explains how different bidders could behave in auction marketplaces.

The auction theory can be applied to both real and realistic markets. By using this approach, however, the calculation of equilibrium bidding strategies for auction games becomes challenging as there are multiple items on sale with values that depend upon each other. When no player (or bidder) can enhance their selected strategy after examining their opponent’s options, the Bayesian Nash equilibrium (BNE) occurs in game theory.

The BNE is thought to be a predictable outcome of a game or auction since it is a stable consequence. When compared to finite complete-information games like rock-paper-scissors, auctions are still difficult to calculate. Because opponents’ values and bids are spontaneous and ongoing, this happens.

Recent studies have introduced several numerical techniques that could be used to master equilibria in auction games. These methods are either based on calculations of pointwise best responses in the strategy space, or they are based on iteratively solving subgames. Their use was restricted mainly to simple single-object auctions.

Researchers at the Technical University of Munich have recently proposed a new machine learning technique that could be used to learn local equilibria in symmetric auction games. This technique was introduced in a paper published in Nature Machine Intelligence and works by representing strategies such as neural networks and then applying policy iteration based on gradient dynamics while a bidder is playing against himself.

The research team has been researching auction theory and exploring its applications for several years now. Their recent study expressly set out to develop a technique based on artificial neural networks and self-play that can automatically adapt equilibrium bidding strategies in auctions.

When the researchers tested their technique, it was found that the BNEs it approximated collided with the analytically derived equilibrium every time it was available. The estimated error rate was also deficient in cases where the analytical balance is still unknown. In the future, the tool they built could further be used to investigate the efficiency of auctions and determine the bidding strategies one may expect from the equilibrium.

In addition to its crucial contribution to the study of auction theory, the technique created by the researchers and his team could be a precious tool for auctioneers, as it could help them to select auction formats and also aid bidders to develop their bidding strategies. For instance, it might be helpful during spectrum auctions, which regulators use worldwide to distribute the rights to transmit signals over specific electromagnetic spectrum bands to different mobile network providers.

They have primarily adopted the standard learning process in neural networks to handle the obstacles of utility functions in their auction models and were also able to prove that the method converges to equilibrium in auctions with just a mild set of assumptions. 

The researchers want to test their method in a variety of circumstances to ensure that it will generalise well in future studies. They also intend to create tools that can automatically compute equilibria on a wider range of game theory-related challenges, including some that go beyond symmetric auction games.

Paper: https://www.nature.com/articles/s42256-021-00365-4

Source: https://techxplore.com/news/2021-09-machine-technique-local-equilibria-symmetric.html

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