On April 7, 2025, The ITU Department of Mathematics Engineering is proud to announce a significant academic achievement within its graduate program. The Ph.D. thesis supervised by Prof. Dr. Burhaneddin İzgi and authored by Dr. Murat Özkaya has been honored with the prestigious Doctoral Special Award. Titled “Matrix Norm Based-Solution Methods and Machine Learning: Stochastic Games and Their Applications”, this groundbreaking research stands out for its successful integration of distinct scientific fields. It makes substantial contributions to the landscape of game theory by effectively bridging classical, rigorous mathematical methods with the predictive power and speed of modern machine learning techniques. This comprehensive study investigates the complex dynamics of game theory, specifically focusing on bimatrix, stochastic matrix, and Markov games. To address limitations in existing literature, the research proposes novel and efficient solution methodologies. Initially, the thesis introduces the Matrix Norm (MN) method specifically for non-zero-sum bimatrix games. It further advances this theoretical concept by extending it to the Extended Matrix Norm (EMN) method. A pivotal contribution of this section is the derivation of a refinement theorem. This theorem is crucial as it establishes significantly more accurate boundaries for game values, thereby making the method highly suitable and robust for iterative computational processes. Demonstrating the versatility and real-world relevance of these theoretical frameworks, the thesis applied them to a critical global issue. The framework was utilized to model the risk of Covid-19 infection across different countries. By employing repeated bimatrix games, the authors were able to analyze and simulate complex behavioral patterns and interaction dynamics observed during the pandemic. A major challenge in game theory is the heavy computational burden associated with large strategy sets. To overcome this, the thesis incorporates a novel neural network architecture. The system is trained on extensive datasets generated via the EMN method. Results show that this network can solve large-scale zero-sum matrix games with remarkable precision, achieving less than 10% relative error. Furthermore, the research enhances the traditional Shapley iteration method for stochastic matrix games by integrating the EMN approach. This integration is proven to significantly reduce the number of required iterations, optimizing the solution process. Finally, the work addresses Markov reward games in decision tree form. It introduces a holistic matrix norm-based solution and incorporates a convolutional neural network for optimal strategy prediction, achieving impressive error rates below 3%. Ultimately, this award-winning thesis offers a robust theoretical and computational toolkit. It demonstrates how machine learning can be strategically leveraged to solve complex, large-scale dynamic games with high efficiency.