Non convex optimization in game theory: Investigation of DC Programming Method for Bimatrix Game Solutions

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.