# Game on Zero Sum

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## Date

2020-06-22

## Authors

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## Publisher

Addis Ababa University

## Abstract

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.

## Description

## Keywords

Game, Zero, Sum