The document discusses the dominance method for solving pure and mixed strategy problems in game theory. It explains that the dominance method eliminates inferior strategies by comparing the payoffs between two strategies - if one strategy always has equal or higher payoffs, it dominates and the inferior strategy can be removed. The example shows applying this method by comparing rows and columns to simplify a game down to a 2x2 matrix, then using the odds method formula to find the value of the game and optimal strategies.

1. DOMINANCE METHOD
Dominance method is also
applicable to pure strategy and
mixed problems. In pure
strategy the solution is obtained
by itself while in mixed
strategy it can be used for
simplifying the problem.

2. PRINCIPLE OF DOMINANCE
 The Principle of Dominance states that if the strategy of
a player dominates over the other strategy in all
condition then the later strategy is ignored because it
will not effect the solution in any way. For the gainer
point of view if a strategy gives more gain than another
strategy, then first strategy dominate over the other and
the second strategy can be ignored altogether.
 Similarly from loser point of view, if a strategy involves
lesser loss than other in all condition than second can be
ignored. So determination of superior or inferior strategy
is based upon the objective of the player. Since each
player is to select best strategy, the inferior strategies can
be eliminated.

3. STEPS OF P.O.D
 STEP1:- compare two rows and eliminate or
delete the row which is having elements less
than or equal to the other raw.
 STEP2:- compare two columns with each
other, the column with least or equal
elements will be kept and other columns will
be deleted.
 These steps will be repeated till we reach to
(2*2) matrix and then we will apply saddle
point or odds methods to find the value of
game.

4. EXAMPLE OF DOMINANCE PRINCIPLE
 Firm B B1 B2 B3 B4
Firm A A1 35 65 25 5
A2 30 20 15 0
A3 40 50 0 10
55 60 10 15
A4

5. SOLUTION:-
 STEP1:- Row 2nd is less than row 1st & row
2nd dominant.
35 65 25 5
40 50 0 10
55 60 10 15
 STEP2:- Column 2nd is greater than the
column 1st & now column 2nd will be
deleted.
35 25 5
40 0 10
55 10 15

6.  STEP3:- Again we will compare 2nd & 3rd
row and than row 2nd is less then the row
3rd & row 2nd is dominant, so it will
deleted.
35 25 5
55 10 15
 STEP4:- Again we will compare the
column 1st and 2nd and now the column 1st
is greater then the 2nd so it will be deleted.
25 5
10 15

7.  Now if saddle point is not occur we will
apply the ODD’S FORMULA to find out
the dominance principle.
a1 a2 =(b1-b2)
b1 b2 =(a1-a2)
(a2-b2) (a1-b1)
V= a1 (b1-b2) +b1 (a1-a2) /(b1-b2) + (a1-a2)

8.  After applying the odd formula, we will
get:
= 25(5) + 10(20) / (5) + (20)
= 125+200/25
=325/25
=13
Strategies for every player:-
 A1= b1-b2/b1-b2+a1-a2
= 5/5+20
=5/25
=1/5

9.  A2= a1-a2/b1-b2+a1-a2
=20/5+20
=20/25
= 4/5
 B1=a1-b2/a2-b2+a1-b1
=10/10+15
=10/25
=2/5
 B2=a1-b1/a2-b2+a1-b1
=15/10+15
=15/25
=3/5