Economics Game Theory

1. GAME THEORY: INTRODUCTION
Game theory is the
study of how optimal
strategies are
formulated in conflict.

2. WHAT IS A GAME?
 A game refers to a situation in which two
or more players are competing having
different goals or objectives

3. IMPORTANT FACTORS
 Number of players
 Total Payoff
 Strategy
 (a) Pure strategy
 (b) Mixed Strategy
 Optimal Strategy

4. TWO PERSON ZERO SUM GAME
 Involving only two players.
 The gains made by one equals the loss
incurred by the other.

5. TWO PERSON ZERO SUM GAME :
PAYOFF MATRIX

6. WHAT IS MINIMAX AND MAXIMIN
PRINCIPLE ?
 Minimax–Maximin principle is a decision
making criterion that specifies how the
players must select their respective
strategies

7. RULES FOR DETERMINING A SADDLE
POINT
 Select the lowest element of each row of the
payoff matrix and mark it as (*) .
 Select the greatest element of each column
of the payoff matrix and mark it as (º) .
 The element in the payoff matrix marked with
(*) and (º) both is a saddle point of the payoff
matrix.

8. TWO PERSON ZERO SUM GAME
(WITHOUT A SADDLE POINT)
 Player A has strategy A1and A2
 Player B has strategy B1and B2
 A chooses strategy A1 with the probability
p1and A2with probability p2 = 1-p1
 B plays strategy B1with probability q1and
strategy B2with probability q2= 1-q1

9. PAYOFF MATRIX OF A AND B

10. Evaluation of Probabilities

11. OPTIMAL MIXED STRATEGIES OF
A AND B

12. DOMINANCE
 What is a Dominant Strategy?
 A particular strategy that is found to be
preferable over other strategies available to a
player is called the “dominant strategy” for
that player.

13. PRINCIPLES OF DOMINANCE
 RULE 1
 If all the elements in a row ( say ith row )
of a pay off matrix are less than or equal
to the corresponding elements of the
other row ( say jth row ) then the player A
will never choose the ith strategy then we
say ith strategy is dominated by jth
strategy and will delete the ith row.

14. PRINCIPLES OF DOMINANCE
 RULE 2
 If all the elements in a column ( say rth
column ) of a payoff matrix are greater
than or equal to the corresponding
elements of the other column ( say sth
column ) then the player B will never
choose the rth strategy or in the other
words the rth strategy is dominated by the
sth strategy and we delete rth column.

15. PRINCIPLES OF DOMINANCE
 RULE 3
 A pure strategy may be dominated if it is
inferior to average of two or more other
pure strategies.