A unified dominance rule framework for deterministic, probabilistic, multi-criteria and game-theoretic decision-making

Decision-making models vary according to certainty, uncertainty, and strategic interaction. This paper develops a unified mathematical framework that integrates deterministic, probabilistic, multi-criteria decision-making (MCDM), and game theory-based models using the dominance rule. The dominance rule systematically eliminates inferior alternatives, simplifying complex decision matrices. A general M×N payoff matrix formulation is introduced, and algorithms are developed for each decision-making type. Through a structured 5×5 payoff example, the effectiveness of dominance elimination, expected value comparison, weighted scoring, and Nash equilibrium analysis is demonstrated. Results show that dominance-based simplification provides computational clarity and consistent optimal strategy identification across diverse decision environments.