GAME THEORY - Problems on Dominance principle

GAME THEORY - Problems on Dominance principle

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 2 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.

3. 3 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:

4. 4 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: 5 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.

6. 6 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.

7. 7 Example problem Of Dominance Principle. Firm A\ firm B B1 B2 B3 B4 A1 35 65 25 5 A2 30 20 15 A3 40 50 10 A4 55 60 10 15 Problem

8. 8 Solution: Step1: Row 2 nd is less than row 1 st .So row 2 nd is dominant or deleted 35 65 25 5 40 50 10 55 60 10 15 Step2: Column 2 nd is greater than the column 1 st and now column 2 nd will be deleted. 35 25 5 40 10 55 10 15

9. 9 Step3: Again we will compare 2 nd & 3 rd row and than row 2 nd is less than the row 3 rd & row 2 nd is dominant,so it will deleted. 35 25 5 55 10 15 Step4: Again we will compare the column 1 st and 2 nd and now the column 1 st us greater than the 2 nd ,so it will be deleted. 25 5 10 15

10. 10 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)

11. 11 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

12. 12 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 . .

13. 13 Reference : http://www.universalteacherpublications.com . https://cbom.atozmath.com https://study.com

14. THANKS!