This document discusses the principle of dominance in game theory. The principle states that if one strategy gives a player a better outcome than another strategy in all situations, the inferior strategy can be eliminated. There are two steps to applying the principle of dominance: 1) compare rows and eliminate rows with lower values, and 2) compare columns and eliminate columns with lower values. This process simplifies the game matrix until a solution can be found using saddle point or odds methods. An example problem demonstrates applying the dominance principle to eliminate inferior strategies row-by-row and column-by-column until the game is solved.

1. GAME THEORY
problem s on Dominance
principle
Under the guidance of
Sundar B. N.
Asst. Prof. & Course Co-ordinator
GFGCW, PG Studies in Commerce
Holenarasipura
Suma M M
2 nd m.com

2. “
Dominance principles
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Dominance principle 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.

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1. The principle of dominance states that If the
strategy of a player dominates over the other Strategy
in all conditions than the later strategy is ignored
because it will not effect the solution is any way.For
the gainer point of view if a strategy gives more gain
than the another strategy, then first strategy dominate
over the other and the second strategy can be ignored
altogether.
Principle Of Dominance:

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2. 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.

5. Steps Of Principle Of Dominance:
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Step1:
Compare two rows and eliminate or delete the row
which is having elements less than or equal to other row
Step2:
Compare two columns with each other,the column
with least or equal elements will be kept and other
columns will be deleted.

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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.

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Example problem Of Dominance Principle.
Firm A
firm B
B1 B2 B3 B4
A1 35 65 25 5
A2 30 20 15 0
A3 40 50 0 10
A4 55 60 10 15
Problem

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Solution:
Step1: Row 2nd is less than row 1st.So row 2nd is
dominant or deleted
35 65 25 5
40 50 0 10
55 60 10 15
Step2: Column 2nd is greater than the column 1st
and now column 2nd will be deleted.
35 25 5
40 0 10
55 10 15

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Step3: Again we will compare 2nd & 3rd row and than
row 2nd is less than 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 us greater than the 2nd ,so it will be
deleted.
25 5
10 15

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

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

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

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Reference:
• http://www.universalteacher
publications.com.
• https://cbom.atozmath.com
• https://study.com

14. THANKS!