GAME THEORY : SOLVING TWO PERSON AND ZERO - SUM GAME PRESENTED BY Ms.K.PARIMALADEVI ASSISTANT PROFESSOR DEPARTMENT OF MATHEMATICS(SF) ERODE ARTS AND SCIENCE COLLEGE

GAME THEORY : SOLVING TWO PERSON AND ZERO - SUM GAME PRESENTED BY Ms.K.PARIMALADEVI ASSISTANT PROFESSOR DEPARTMENT OF MATHEMATICS(SF) ERODE ARTS AND SCIENCE COLLEGE.

Game Theory : Solving Two Person and Zero - Sum Game.

PROPERTIES OF A GAME. 1. There are finite numbers of competitors called ‘players’.

outcome such that no player knows his opponents strategy until he decides his own strategy..

8. The expected pay off when all the players of the game follow their optimal strategies is known as ‘value of the game’. The main objective of a problem of a game is to find the value of the game..

COMPETITIVE GAME. A competitive situation is called a competitive game if it has the following four properties.

assumed to be made simultaneously i.e. no player knows the choice of the other until he has decided on his own..

STRATEGY. The strategy of a player is the predetermined rule by which player decides his course of action from his own list during the game..

Solving Two-Person and Zero-Sum Game. Two-person zero-sum games may be deterministic or probabilistic. The deterministic games will have saddle points and pure strategies exist in such games. In contrast, the probabilistic games will have no saddle points and mixed strategies are taken with the help of probabilities..

Definition of saddle point. A saddle point of a matrix is the position of such an element in the payoff matrix, which is minimum in its row and the maximum in its column..

If their appears an element in the payoff matrix with a circle and a square together then that position is called saddle point and the element is the value of the game..

Example-1 Solve the payoff matrix. Player B. Player A.

SOLUTION.

ANSWER. Strategy of player A – II. Strategy of player B – III.

Example-2 Solve the payoff matrix. Player A. Player B.

SOLUTION.

SOLUTION. Strategy of player A – A2. Strategy of player B – B3.