Non convex optimization in game theory

The search for the Nash equilibrium is a fundamental problem in game theory. In this manuscript, we focus on computing this equilibrium for bimatrix games with mixed strategies. Our objective is to investigate the application of nonconvex optimization techniques, specifically DC programming (Difference of Convex functions) and the DCA (DC Algorithm). The proposed approach involves reformulating the game as a linear complementarity problem, modeling it as an optimization problem, and finally solving it using DC programming and DCA. A comparative analysis with the well-known Lemke-Howson algorithm is also provided.

Autorentext

Aicha Anzi is an associate professor in the Operational Research Department of University of Bejaia, Algeria. She received her PhD degree in Applied Mathematics in 2018 and her HDR in 2021 at the University. Her teaching and research interests are in the areas of mathematical programming, bilevel optimisation and game theory.