Game Theory: Please show your work and explain the answers to help me understand
ID: 1149298 • Letter: G
Question
Game Theory: Please show your work and explain the answers to help me understand the process
Consider the following normal form game between A and B. Use iterated elimination of dominated strategies, if possible, to find the solution to the three games 1. C1 5, 4 X, 12 C2 C3 A R1 R2 7,7 3, 10 1, Y 9, 10 a. b. C. Let X = 5 & Y = 2 . Find the solution Let X = 6 & Y = 9. Find the solution Let X = 3 & Y 11. Find the solution 2. Consider the following game between A and B A up down Left 5, 5 4,Z Right 2, 0 Find precise restrictions on the allowable values of Z so that it is guaranteed that this game cannot be solved using IEDSExplanation / Answer
Answer for 1)
a) If X=5 Y=2
If we compare Player A's action (R1,R2) There is no dominance as 5=5,7>3 &1<9 hence no dominatin strategy available with player A
If we compare Player B's action (C1,C2,C3) then we can see that C1 strictly dominates C3 and C2 weakly dominates C3 hence we C3 is dominated by C1 hence we can eliminate C1.
Now the matrix we have is
C1 C2
R1 (5,4) (7,7)
R2 (5,12) (3,10)
In this reduced form we have NE at (R2,C1)
Answer for part b
x=6, Y=9
If we compare Player A's action (R1,R2) There is no dominance as 5<6,7>3 &1<9 hence no dominatin strategy available with player A
If we compare Player B's action (C1,C2,C3) then we can see that C3 weakly dominates C2 Hence C2 can be eliminated
Now the matrix we have is
C1 C3
R1 (5,4) (1,9)
R2 (6,12) (9,10)
In this reduced form we have NE at (R2,C1) again.
Answer for Part C
X=3, Y=11
If we compare Player A's action (R1,R2) There is no dominance as 5>3,7>3 &1<9 hence no dominatin strategy available with player A
If we compare Player B's action (C1,C2,C3) then we can see that C3 weakly dominates C2 hence we can eliminate C2
Now the matrix we have is
C1 C3
R1 (5,4) (7,9)
R2 (3,12) (3,10)
In this reduced form we have NE at (R1,C3)
Answer for Q2
If No Iterated elimination is allowed then for Player A "Z" should be more than 2 & for player B "Z" should be less than 3 hence combining both these inequalities we get the region where Z can take any value
2<Z<3
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