Master's thesis - Learning in Purified Games

10.07.2025, Abschlussarbeiten, Bachelor- und Masterarbeiten

This thesis will analyze the effect of "purifying" games on the convergence properties of learning algorithms in a multiagent setting.

In many markets, algorithms are increasingly being used for adapting companies’ pricing strategies. In microeconomics, game theory has long been used to model markets. With the development of computational power and more sophisticated algorithms, learning players become an interesting avenue of research. Learning in markets (games) creates a complex mulitagent setting in which the learning dynamics are generally difficult to predict. Prior work (Mertikopoulos and Sandholm 2016; Giannou et al. 2021) suggests that strict Nash equilibria play an important role for convergence in finite normal-form games while mixed Nash equilibria are instable.

In this context, we analyze the idea of ”purification”, introduced by Harsanyi (1973). Intuitively, we perturb the game slightly to resolve ties between actions, thus turning mixed Nash equilibria into pure Nash equilibria.

This project should experimentally evaluate the effect of purification. With randomly perturbed payoff matrices under perfect and imperfect information, we simulate the dynamics of learning agents and observe their convergence behavior.

This topic combines complex ideas from game theory with implementation. I need a highly motivated student with proper math skills (for the context), basic knowledge of game theory, and some implementation skills. For this reason, I will be selective with applications.

If you are interested in the topic, please send me an (informal) email with your CV and transcript of records. There is also a more detailed description of the project available.

Kontakt: julius.durmann@tum.de