Unit-III-1-GT

8/9/2019 Unit-III-1-GT

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Operations Research

MBA-024


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GAME THEORY

UNITIII


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This is a competitive model.

In LP we have been dealing with a situationknown as Internal Conflict.

Theory of Games is a technique of dealing with

external conflict. There are a number of firms operating in an

industry producing different brands of the

product.

The objective of each firm is to have the

maximum slice of the market.


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Game

A competitive struggle among n players for a

common objective.

In an ordinary game, 2 teams are pittedagainst one another; both employ different

strategies to achieve their objective.

However, in business setting there may be

more than 2 firms.

The objective of a Game is to win without

cheating.


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Important Characteristics of a

Game1. There are a finite number of participants.

2. Each participant has only a finite number of

strategies available.3. Each player knows the strategies available to

the adversary, but he does not know which

strategy will the adversary adopt.

4. All possible outcomes are calculable.


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A strategyis a decision rule by which a player

chooses his course of action. When a player spends all his time or resources

on a particular course of action, he is said to

have employed a pure strategy.

When a player spends his time or resources on 2

or more courses of action, he is said to have

employed a mixed strategy.


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The outcome which is quantified when players

adopt a specific course of action is a payoff. The element denoting this payoff is a payoff

element.

Payoff

matr

ixis the matrix constituted by the

payoff elements.

The value of the game is the average winning of

a player per play over a series of plays.


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Two Person Zero Sum Game

Algebraic sum of the gains and losses of the

players is zero.

That is, the gain of one player is the loss of theother.


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The game is given in the form of a payoff matrix:

Rows represent the strategies available to A.

Columns represent the strategies available to B.

Positive payoff elements mean gain to A.

Negative payoff elements mean loss to A.


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The game is played on the assumption that both

players are conservative in nature. Objective of A is to ensure for himself a

minimum gain which cannot be reduced by

whatever B does. (irreducible gain)

Object of B is to ensure that he does not lose

more than a certain amount.


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Strategy recommended for A: Maximin.

Strategy recommended for B: Minimax.

Maximin: maximum of the row minima.

Minimax: minimum of the column maxima.


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Principle of Dominance

If all the elements in the ith row are less than

or equal to the corresponding elements of the

jth row, then the ith strategy is said to be

dominated by the jth strategy.

If all the elements in the rth column are

greater than or equal to the corresponding

elements of the sth column, then the rth

strategy is said to be dominated by the sth

strategy.


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Odds Method

Subtract the smaller payoff in each row from

the larger one and the smaller payoff in each

column from the larger one.

Interchange each of these pairs of subtracted

numbers found in previous step.

Put each of the interchanged numbers over

the sum of the pair of numbers.

Simplify the fraction to obtain the required

strategies.


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Graphical Method

Unit-III-1-GT

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