The field of neural network game theory is moving towards a deeper understanding of the underlying geometric structures that govern the behavior of min-max games. Recent research has identified hidden convexity and overparameterization as key factors that contribute to the convergence of simple gradient methods in non-convex non-concave objectives. This has led to the development of new theoretical frameworks and algorithms that can guarantee global convergence to a Nash equilibrium in a broad class of games. Furthermore, researchers are exploring new classes of games, such as monotone near-zero-sum games, that can be used to model practical scenarios and improve the efficiency of gradient-based algorithms. Notable papers in this area include: Solving Neural Min-Max Games, which provides a theoretical framework for understanding the convergence of gradient methods in non-convex min-max games. Monotone Near-Zero-Sum Games, which defines a new class of games that can be used to model practical scenarios and improve the efficiency of gradient-based algorithms. Diagonalizing the Softmax, which provides an in-depth characterization of cross-entropy optimization dynamics and introduces a new technique for analyzing these dynamics.