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Seminar | Mathematics and Computer Science

Solving Multi-Leader-Follower Games by Smoothing the Follower’s Best Response

LANS Informal Seminar

Abstract: The multi-leader-follower game is a particular subset of classical game theory. These models serve as an analytical tool to study the strategic behavior of individuals in a noncooperative manner. In particular, the individuals (players) are divided into two groups, the leaders and the followers, according to their position in the game. Mathematically, this leads to optimization problems with optimization problems as constraints. The challenge in leader-follower problems are due to possible nonsmoothness in the constraints.

We derive the best response function of the follower, which we regularize by using a suitable smooth regularizer. We discuss existence of Nash equilibria of the smoothed problems and deduce a numerical algorithm based on the smooth formulation. We further present an update of the primal variables for efficient computation. Finally, we present numerical results to illustrate our approach and give an outlook to future research.

This seminar will be streamed.