THE GAME THEORY AND SIMULATION WITH FINITE MIXED STRATEGY OF TWO-PLAYERS ZERO SUM GAME
J. O. OKORO *
Department of Industrial Mathematics and Physical Science, College of Science and Engineering, Landmark University, Omu-Aran, Kwara, Nigeria.
A. OGHENEKEVWE
Department of Mathematics, Federal University, Oye-Ekiti, Ekiti State, Nigeria.
N. K. OLADEJO
Department of Industrial Mathematics and Physical Science, College of Science and Engineering, Landmark University, Omu-Aran, Kwara, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
We explain the concept and theory behind game theory and simulation. How game theory can be used to simulate competition existing in the market, business organisation, and even in the management setting. The game we consider here is the zero-sum game. We show types strategies game players in a real market situation should adopt. We show how we minimise our losses and maximise our gain by introducing the concept of maxmin and min-max. We analysed finite payoff matrix of a zero sum-game using some fundamental principles. We apply the theory of mixed strategies with a game without a saddle point. We show that the dual linear programming problem of one player is the linear programming problem of the other player. The four methods available in solving mixed strategy of two-players zero-sum game was analysed by showing the application of linear programming problem to game theory. We use these techniques to simulate possible mixed strategy of two-players zero-sum game using the Microsoft excel package.
Keywords: Games and decisions, payoff, strategies, saddle points, players