Recent breakthroughs of learning decision-making algorithms were achieved in the area of Reinforcement Learning [1, 2]. However, training systems with more than one agent remains a challenge due to resulting non-stationarity of the decision-process [3]. You can study related problems during your thesis in complex but fast environments[4] that are already embedded into our framework.

Requirements: Python, optimization, basics in reinforcement learning, machine learning and / or game theory.

The sharing economy depends on the development of the sharing platform. Different platforms (e.g., ride-hailing, freight exchange, kidney exchange, resource allocation, ... ) have different characteristics. We are committed to abstracting mathematical models from reality to simulate, analyze and provide theory. Research issues include but are not limited to matching strategies, pricing issues, and online prediction.

Requirements: advanced programming skills (e.g., Python, Matlab, at least one), mathematics, operation research

As part of our research on electricity markets and our involvement in the Kopernikus SynErgie project we are developing large-scale and realistic models for clearing and pricing on electricity markets. In particular, we want to build on several libraries, implementations, and data sources to create a code base that enables extensive testing and impact analysis of different market designs.   

Requirements: advanced programming skills (Python, possibly Julia), mathematical optimization

Electricity Market Design: Electricity market design is dynamic in its nature and has recently been exposed to fundamental changes due to the integration of renewable energy resources. We examine sustainable market designs and the underlying allocation and pricing problems as part of the Kopernikus SynErgie project. 

Pricing in non-convex markets: Although nonconvex markets (such as electricity markets) are widespread, finding appropriate prices is not trivial. We study different pricing approaches and associated properties.

Requirements: programming skills, operations research

While the computation of Nash Equilibria in matrix games is a PPAD-complete problem, there are several algorithms that compute exact Equilibria for such games.  There are several possibilities for a thesis in this area: a literature review on existing algorithms, or an implementation of a particular algorithm applied to some specific games. Depending on the chosen topic, both bachelor and master theses would be possible.

Requirements: experience in algorithms, mathematics, (depending on the project:) good programming skills in the language of your choice

Numerical Methods for Variational Inequalities

Nash equilibria can be formulated as solutions of variational inequalities. We are interested in numerical methods which are used for such problems (e.g. methods for for monotone VI) and their applicability to equilibrium problems.  Depending on the focus of the topic one could implement different algorithms (e.g., extragradient methods), give an overview of different methods and their convergence behaviour (literature review), or apply such a method to our framework in order to compute Bayes Nash equilibria in auction games.

Requirements: good mathematical background, interest in algorithms and optimization (e.g. gradient descent methods), ideally basic knowledge on game theory, programming skills (pref. in Python)

A more detailed proposal can be found here.

A common assumption in economic theory is that market participants follow an equilibrium strategy. However, it is questionable whether agents receive a stable state, i.e., a Nash equilibrium, in highly dynamic and complex environments. Thus [1] proposed that agents follow a no-regret learning procedure to derive their strategy. Based on that, they developed a structural estimation procedure and showed that the resulting strategies fit observed bevaior in auction experiments well. The goal of this thesis topic is to develop a neural-network based learning framework on the basis of regret-minimization. 

Requirements: good programming skills (pref. in Python and Pytorch), understanding of fundamental game theoretical concepts

[1] Nekipelov, D., Syrgkanis, V., & Tardos, E. (2015, June). Econometrics for learning agents. In Proceedings of the sixteenth acm conference on economics and computation (pp. 1-18). 

Auctions and contests are important applications of game theory. However, the empirical literature showed that bidders do not follow their predicted equilibrium strategies, but instead tend to overbid [1, 2]. A possible explanation is that bidders are not risk-neutral, but follow some behavioral concept, like risk-aversion or post-auction regret. In a current project, we developed an estimation framework to quantify these concepts [3]. Possible thesis topics could extend this structural estimation approach. Besides, some authors propose other equilibrium concepts, like the impulse-balance-equilibrium [4], where bidders adjust their strategies according to some regret term. The goal of a thesis would be to develop an algorithm to estimate the bidder-specific parameters of these equilibria. 

Requirements: basic game theoretical understanding, interest in behavioral economics and learnin in games, good programming skills (pref. in Python or R)

[1] Dechenaux, E., Kovenock, D., & Sheremeta, R. M. (2015). A survey of experimental research on contests, all-pay auctions and tournaments. Experimental Economics, 18(4), 609-669.

[2] Kagel, J. H., & Levin, D. (1993). Independent private value auctions: Bidder behaviour in first-, second-and third-price auctions with varying numbers of bidders. The Economic Journal, 103(419), 868-879.

[3] Ewert, M., Heidekrüger, S., & Bichler, M. (2022, May). Approaching the Overbidding Puzzle in All-Pay Auctions: Explaining Human Behavior through Bayesian Optimization and Equilibrium Learning. In Proceedings of the 21st International Conference on Autonomous Agents and Multiagent Systems (pp. 1586-1588).

[4] Ockenfels, A., & Selten, R. (2005). Impulse balance equilibrium and feedback in first price auctions. Games and Economic Behavior, 51(1), 155-170.