Optimal Mixed Strategy Selection for Two-Person Zero-Sum Games under Interval-Fuzzy Payoff Uncertainty

Objectives: To overcome the shortcoming of being limited-time interval derivative based game theory in dealing with the issue of uncertain payoffs and to suggest an optimization-based model of deriving plausible forms of mixed strategies in zero-sum games between two players. Methods: A hybrid interval-fuzzy payoff representation is proposed to describe uncertainty in more impressive way. The value of standard norm-based bounds is computed on approximate game values. There is a formed strategy selection process employed that is based on optimization where the derived bounds are used to derive the upper and lower thresholds of mixed strategies (psup and pinf). These are realistic interval matrices and synthetic simulations. Findings: The suggested approach does not require solving linear programming problems and it has a competitive set of game values as compared to conventional approaches. The strategy on the 3 × 3 matrix games provided consistent approximate values [2.666, 5.000]. The algorithm is scalable and analyzable like bigger games for 10 × 10 matrix. Novelty: The paper presents the first intervalfuzzy payoff approach which maintains both the interval width and the fuzzy confidence at the same time in the zero-sum games. A bounding mechanism that is norm based is created to estimate game values without the use of linear programming, allowing analysis of large matrices on a scale. Theoretical results are now determined new to interval fuzzy saddle-point conditions, mixedstrategy interval convexity and mixed-strategy interval duality-gap control. Keywords: Two-Person Zero-Sum Game; Interval-Fuzzy Matrix; Mixed Strategy; Norm-based Estimation; Saddle Point; Game Theory