Philip Hierhager

I am a researcher at the Technical University of Munich working on optimization, variational inequalities, dynamical systems, learning in games, stochastic approximation, and measure-valued methods.

Research Interests

Optimization and variational inequalities
Dynamical systems and Lyapunov methods
Learning in games and multi-agent systems
Stochastic approximation and online learning
Infinite-dimensional and measure-valued methods
Newtonian and Hamiltonian dynamics on metric spaces

Thesis Supervision

If you are interested in writing a Bachelor’s or Master’s thesis, feel free to get in contact.

news

Oct 19, 2026	Symposium update: I will present our joint project, Learning and Dynamics in Stochastic Multi-Agent Systems, at the Scientific Opening Symposium of the Heilbronn Data Science Center in Heilbronn on November 2, 2026. Led by Jingui Xie, Martin Bichler, Christian Kuehn, and Christoph Knochenhauer, the project combines data science, AI, operations research, management, and economics to study learning and adaptation in stochastic multi-agent systems, with applications in healthcare, service systems, and platform economies.
Oct 19, 2026	Workshop update: I will attend the Optimization in AI workshop at RICAM in Linz, Austria, from November 23–27, 2026, as part of the Special Semester on AI in Scientific Computing.
Oct 15, 2026	New preprint: How language model agents reshape price competition, joint work with Martin Bichler, Kassian Köck, and Fabian Pieroth, is now available on arXiv.

selected publications

arXiv

How language model agents reshape price competition

Martin Bichler, Philip Hierhager, Kassian Köck, and 1 more author

2026

Abs arXiv PDF

This paper studies language model pricing agents in repeated Bertrand competition. Their behavior depends on deployment choices: agents using raw market histories that include rival prices can sustain supracompetitive prices in self-play, while agents using summarized histories of their own profits tend toward competitive prices. Mixed deployments can produce dynamic pricing regimes that keep both competitors’ prices above marginal cost.
arXiv

Liouville-Preserving Hamiltonian Scattering on Finite Metric Graphs

Philip Hierhager

2026

Abs arXiv PDF

This paper studies deterministic Hamiltonian dynamics on finite metric graphs. Since energy conservation alone does not determine how a trajectory continues through a branching vertex, the paper introduces energy-preserving vertex scattering maps. The resulting edge-and-vertex dynamics define a global measurable flow that preserves energy and the quotient Liouville measure.