Existence of optimal strategies in a normalized interval matrix game and applications

Abstract Vagueness in the real-world problem performs a significant role in determining the existence of a feasible solution to the problem. This vagueness in the model may be handled by considering the parameters of the problem as a closed interval. In this competitive world, game models with uncertain payoffs can successfully handle conflicting real-world problems. Therefore, a two-player zero-sum game model in which payoffs vary in a range is considered. Then, the existence of saddle point (pure strategy) and dominance rules are discussed for the game model, and mixed strategy is defined in the case of non-existing saddle point. Thereafter, a methodology has been developed to discuss the existence of weak and control strategies in the interval game model. Furthermore, we obtain the optimal value of the game model as a deterministic number. Finally, the developed methodology is successfully implemented to solve real-world investment problems in the stock market and obtain the optimal strategy to achieve the maximum return.