Game On Zero Sum

A game with two rational players in which the gain payo for one is loss for thernother is called two person zero-sum game. i.e the sum of payo s for the two playersrnare zero. Two person zero-sum game with nite sets of strategies are called matrixrngames. Rational players always seeks to maximize his payo by choosing a bestrnstrategy. If the matrix of the game is payo for Player 1, then player 1 at worstrncase guarantee himself to maximize the minimum loss of player 2. Similarly playerrn2 at worst case guarantee himself to minimize the maximum payo player 1. Anyrnmixed matrix game has optimal solution which is called saddle point in mixedrnstrategies.rnThis project is focuses only on two person zero-sum game part of Game Theoryrnwith nite player strategies and present how to nd the optimal value of the gamernor optimal solution strategies(saddle point) of the players. To nd optimalityrnsolution method of primal(dual) linear programming problem and dominance strategyrnmethods are used. The objective is to nd the optimal strategies of the players inrntwo person zero-sum game and optimal value of the game.

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