GAME THEORY - Problems on Dominance principle
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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.
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 0 A3 40 50 0 10 A4 55 60 10 15 Problem
- 8. 8 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
- 9. 9 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
- 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
- 13. 13 Reference: • http://www.universalteacher publications.com. • https://cbom.atozmath.com • https://study.com
- 14. THANKS!