Anna ThünenInstitut für Geometrie und Praktische Mathematik
phone:+49 241 80-94559
fax:+49 241 80-693951
- Multi-Leader-Follower Games in Function Space This project aims to design efficient and problem tailored numerical solution methods for certain classes of MLFGs in function space accompanied by the theoretical analysis of these problems. While in a classical Nash equilibrium problem (NEP) we have several players that simultaneously make a decision which influences their own outcome and that of the others, in a multi-leader-follower game (MLFG) the group of players is split into the so-called leaders deciding first and followers reacting to this. This hierarchical game has various applications e.g. in telecommunications, traffic networks and electricity markets. It can be seen as an extension of the single-leader-multi-follower (Stackelberg) game or mathematical program with equilibrium constraints (MPEC). Though by now much is known about NEPs and MPECs in finite dimensions and lately also in function space, this is not the case for MLFGs.
- Multiscale Control Concepts for Transport-Dominated Problems In recent years, the description of controllable (or active) particle systems using methods of kinetic gas theory has been achieved and allows now to tackle a wide range of applications as for example traffic flow. In this research project, the inherent hierarchy exploited extensively in kinetic theory for theoretical and numerical considerations will be investigated in order to develop novel analytical and numerical methods for control problems posed on multiple scales as well as under aspects of non-smoothness in the control. The work program includes the analysis of consistent optimality conditions within the model hierarchies, numerical analysis for control aspects relevant in particular on the highest level of the model hierarchy, as well as the development of numerical methods for time-dynamic non-smooth optimization problems on all levels. In addition to the sensitivity of non-smooth kinetic equations, the multi-scale nature of the equations raises questions for boundary control problems of nonlocal hyperbolic equations and switching systems.
Michael Herty, Sonja Steffensen, and Anna Thünen: Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower’s Best Response
Sonja Steffensen and Anna Thünen: An Explicit Nash Equilibrium to a Multi‐Leader‐Follower Game (PAMM 2019)
Jan Becker, Alexandra Schwartz, Sonja Steffensen and Anna Thünen: Extensions of Nash Games in Finite and Infinite Dimensions with Applications, In: M. Hintermüller et al. (eds.), SPP1962 Special Issue, Birkhäuser, 2019.
- I co-organize a session on mean field games for 19th International Symposium on Dynamic Games and Applications in Porto June 16-19, 2020. [Postponed]
- I am Vice President of the Student Chapter of SIAM in Aachen. Check out our blog.
- I co-organized MESIGA 2019 [Meeting of European SIAM and GAMM Chapters] which took place in Aachen September 9-11, 2019.
- I organized the session Nash Equilibrium Problems and Extensions (hierarchy, dynamics and applications) for ICCOPT in Berlin August 5-8, 2019.
- I served as referee for Mathematics of Computation.
- Optimization C (Continuous Optimization), Organization and exercise sessions, winter term 2020/21
- Seminar: Differential Games, Organization, winter term 2018/19
- Mathematik I/II (für Bauing., Umwelting., Wirtschaftsing. FR Bau, Mobilität und Verkehr), co-Organization and exercise sessions , winter term 2017/18 - present