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Game theory is the examination of strategic interactions between two or more individuals known as players who act based on their individual self-interest within a framework known as the game.Every player possesses a set of possible actions referred to as strategies, from which they make selections. In a two-person zero sum game, each of the two players has at least two strategies. In such a game problem where both players have no inferior strategies, we can determine the optimal mixed strategies of the game problem by converting it to a linear programming problem and solving itusing the simplex method or variations of it. However, there seem to be very few reported studies on the conversion of LPP to game problem.
This research work is thus centered on the formulation of a linear programming problem as a game problem. We established the conversion of LPP to a skew-symmetric game, as well as the conversion of LPP to a nonsymmetric game. Staying with the relationship that exist between game theory and linear programming, we also considered some existing models on the conversion of game problem to LPP. We compared the results with our proposed model.
The results obtained revealed that our proposed model on the conversion of game problem to LPP produced a higher value of the game compared to the others considered; and thus, producedbetter performance.
