LINEAR PROGRAMMING PROBLEMS AS SKEW-SYMMETRIC AND NONSYMMETRIC GAMES: FORMULATION AND SIGNIFICANCE

Abstract

Game theory models competitive interactions, like military, political, or business conflicts, mathematically. Two-person zero-sum games, where one’s gain equals another’s loss, are central. Optimal strategies are often found by converting these games into linear programming (LP) problems solvable via methods like the simplex algorithm. However, converting LP problems into game formulations is less explored. This study bridges this gap by reformulating LPPs as skew-symmetric and nonsymmetric games. This approach benefits economic applications like comparative advantage and diet problems with positive constraints and prices. Skew-symmetric games’ Super LPP offers computational efficiency due to sparse structures. By enabling bidirectional translation between games and LP, this work expands game theory’s scope and enhances understanding of two-person zero-sum game properties, strategic frameworks, and their mathematical underpinnings