Competitive Strategies of Two Business Players Using Zero-Sum Game Theory Minimax And Mixed Strategy

A quantitative approach is necessary for making optimal decisions because two companies competing in the same market create conditions of strategic interdependence. The purpose of this study is to analyze the competitive strategies of two business actors using zero-sum game theory using the minimax approach and mixed strategies. This study was conducted quantitatively and descriptively with two types of cases used. The first case is a game without a saddle point, which serves as a validation of the theory; the second case is price competition, which can be applied in a real business environment. The analysis was carried out by creating a Payoff matrix, calculating the probability of a mixed strategy, finding the minimum row and maximum column values, and using QM for Windows to validate the results. The results show that in the first case, no saddle point is found, so the mixed strategy is the optimal solution with a probability of P (X1) = 0,8182, P (Y1) = 0,7273, and the game value is 3.4545. In the second case, a saddle point is found in the combination of low-price strategies, making the pure strategy the optimal choice for both players. This finding demonstrates that zero-sum game theory can provide a rational and objective basis for decision-making in situations of direct competition between two business actors.