Thepursuit of sustainability is a paramount objective for both business strategists and policy makers. Game theory provides a robust mathematical framework for modeling competitive and cooperative interactions, making it highly applicable for strategic decision-making in these domains. This paper demonstrates the application of game theory to derive optimal decisionmaking strategies that support the achievement of Sustainable Development Goals (SDGs). It focuses specifically on elucidating arithmetic (oddment) and algebraic methods for solving 2x2 games without a saddle point. The study employs established gametheoretic principles, including the maximin criterion and dominance, to reduce complex games. For 2x2 zero-sum games without a saddle point, detailed derivations of the arithmetic and algebraic methods are presented to compute optimal mixed strategies and the value of the game. Through illustrative examples, the paper confirms the efficacy of these methods in determining optimum strategies. The arithmetic method offers a simplified, computational approach, while the algebraic method provides a rigorous, formulaic solution, both yielding consistent results for player strategies and game value. Game theory is a powerful tool for enhancing strategic decision-making in competitive environments. The derived methods provide a clear and actionable framework for policymakers and managers to formulate optimal strategies, thereby facilitating more effective progress towardssustainabledevelopment objectives.