Aggregative Mixed-Integer Equilibrium Problems: Existence, Approximation, and Algorithms

• Applicants: Professor Dr. Tobias Harks; Professor Dr. Martin Schmidt
• Subject Area: Mathematics ; Theoretical Computer Science
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 543678993

In this tandem-project, we will consider foundational research questions regarding the existence and computability of Nash equilibria for a class of non-convex and aggregative games. Non-convexity usually arises by restricting some decision variables to be integer and the aggregative structure arises by assuming that the payoff function of every player only depends on the own strategy and on an aggregate of the other players' strategies. This class of games captures key characteristics of distributed energy and traffic systems. The goal of the project is to develop the mathematical theory regarding the existence, computability and characterization of pure Nash equilibria for such games. As our main result, we plan to develop algorithms computing equilibria whenever they exist and also design algorithms for resulting bilevel optimization problems, where some objective function over the equilibrium set is being optimized. All of our algorithmic results will be tested on realistic instances within the two application areas mentioned above.

• DFG Programme: Research Grants