Over the past few decades, computer scientists have explored the potential of applying game theory and machine learning (ML), artificial intelligence (AI) to chess, the abstract strategy board game go, or other games in economics, particularly as a framework for explaining strategic interactions in markets and the outcomes that result from them. One of the most common theoretical constructs developed to enable game theory to be applied to economics is auction theory. Auction theory is an application of game theory that specifically describes how different bidders can act on the auction markets. However, when auction theory is applied to real or realistic markets with multiple items for sale and value interdependencies, calculating equilibrium bid strategies for auction games can be challenging. In game theory, Bayesian Nash equilibrium (BNE) occurs when neither player (or bidder) can improve his chosen strategy after considering his decisions with the decisions of the opponent.
The BNE is considered a stable outcome of a game or auction and can serve as a prediction of the outcome, but it is much more difficult to calculate for auctions compared to finite sets of complete information like rock-paper-scissors. Because the values and offers of the opponents are continuous. Previous studies introduced various numerical techniques that could be used to learn balances in auction games. These methods are based on calculations of the best point answers in the strategy space or on iterative solution subsets. Its use was largely limited to simple individual auctions. Researchers at the Technical University of Munich recently developed a new machine learning method that can be used to learn local equilibria in symmetrical auction games. This technique works by rendering strategies like neural networks and then applying policy iterations based on gradient dynamics while a bidder plays against himself.
“Just last year, the Nobel Prize in Economic Sciences was awarded to Paul Milgrom and Bob Wilson for their work on auction theory and design,” Martin Bichler, one of the researchers who carried out the study, told. “Early work by Nobel Prize laureate William Vickrey led to game-theoretical equilibrium strategies for simple single-object auctions, which are based on the solution to differential equations. Unfortunately, more complex multi-object auctions have turned out very challenging to solve and equilibrium bidding strategies are known only for very specific cases.”
