Formulation of Game Model as a Linear Programming Problem using Various Models

Abstract:

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 it using the simplex method or variations of it. In this paper, consideration of some existing models along with our proposed model on the conversion of game problem to LPP was made. We compared the results across the various models considered. 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, produced better performance.