Browsing by Author "Haileslassie, Amha"

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    Game on Zero Sum
    (Addis Ababa University, 2020-06-22) Haileslassie, Amha; Guta, Berhanu (PhD)
    A game with two rational players in which the gain payo for one is loss for the other is called two person zero-sum game. i.e the sum of payo s for the two players are zero. Two person zero-sum game with nite sets of strategies are called matrix games. Rational players always seeks to maximize his payo by choosing a best strategy. If the matrix of the game is payo for Player 1, then player 1 at worst case guarantee himself to maximize the minimum loss of player 2. Similarly player 2 at worst case guarantee himself to minimize the maximum payo player 1. Any mixed matrix game has optimal solution which is called saddle point in mixed strategies. This project is focuses only on two person zero-sum game part of Game Theory with nite player strategies and present how to nd the optimal value of the game or optimal solution strategies(saddle point) of the players. To nd optimality solution method of primal(dual) linear programming problem and dominance strategy methods are used. The objective is to nd the optimal strategies of the players in two person zero-sum game and optimal value of the game.