Felix-Klein-Kolloquium des Fachbereichs

We introduce the basic ideas of Nash equilibrium problems and explain why branch-and-bound methods from global optimization do not seem to be an adequate solution approach. However, taking a proper persepective, for continuous box-constrained non-convex Nash equilibrium problems we are able to present the first spatial branch-and-bound method for the computation of the set of all epsilon-Nash equilibria with an approximation guarantee. Thereby, the existence of epsilon-Nash equilibria is not assumed, but the algorithm is also able to detect their absence. We formulate convergence results for the proposed algorithm, and report our computational experience.