Dominance method
- 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