Multi-Leader-Follower Games in Function Space

Description

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. We start with the theoretical investigation (existence, uniqueness and suitable approximations of Nash equilibria) of finite-dimensional (i.e. static) MLFGs. Next, we will develop new numerical methods for the static MLFGs, that admit solutions, which avoid the drawbacks of existing methods. These outcomes of the first period of the project are not only of interest by themselves, but will serve us in the main part as starting point for the theory as well as the design of numerical solution methods for the dynamic (time-dependent) MLFG. Additionally, in parallel, applications will be considered to build a test library for our algorithms that will also be made publicly available.

Publications

No publications from this project yet.

Preprints

No preprints from this project yet.

Research Area

Modeling, problem analysis, algorithm design and convergence analysis

The focus of this area is on the development and analysis of genuinely non-smooth models in the sciences in order to properly capture real-world effects and to avoid comprising smoothing approaches. In simulation and optimization this requires to advance set-valued analysis and the design of robust algorithms for non-smooth problems.

Realization of algorithms, adaptive discretization and model reduction

As the target applications of this SPP involve non-smooth structures and partial differential operators, the discretization of the associated problems and robust error estimation are important issues to be address, and proper model-reduction techniques need to be developed.

Members

  • member's portrait

    Prof. Alexandra Schwartz

    Technische Universität Darmstadt
    Principal Investigator
  • member's portrait

    Dr. Sonja Steffensen

    RWTH Aachen
    Principal Investigator
  • member's portrait

    Anna Thünen

    RWTH Aachen
    Research Assistant

Project Related News

  • 25. 07. 2017 : Welcome to our new project member

    Anna Thünen joins Project 21