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Abstract: We will start with a brief discussion of multilevel game models such as bilevel and Stackelberg games or multi-leader-follower games. We will then proceed with the particular application of a dynamic
multilevel game model for the European gas market. Here the (lower-level) players are the traders that act at the nodes of the network where they can nominate, buy or sell gas. The gas flow itself is controlled by the so-called technical system operator (TSO) (upper-level player).

We consider a fully dynamic version of the gas flow using a coupled system of Euler equations to describe the time dependent gas dynamics
in the network. This modelling yields an optimal control problem for the TSO which has to be coupled to the discrete multilevel game model for the traders. Using the particular potential game structure of the
involved discrete Nash games amongst the traders allows us to reduce the multilevel game into a single level problem such that we end up with a bilevel optimal control problem for the TSO.

Title: Optimal Control for ODEs and PDEs: The Turnpike Phenomenon, by Michael Schuster

Title: Probabilistic Constrained Optimization with Differential Equations: An Application to Gas Transport, by Michael Schuster