Stability and Convergence of Optimistic Exponential Weights with Asymmetric Step Sizes in Bimatrix Games

We study bimatrix two-player games and investigate the last-iterate convergence and stability of equilibria for the iterates generated by the optimistic exponential weights method. In contrast to prior work, we allow the step sizes $η_x$ and $η_y$ to differ. Our first main result establishes, under the assumption that the set of fixed points is finite, a sufficient condition for global last-ite…