Reduce the payoff matrix using (weakly) dominated strategies
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Below is the payoff matrix of a game. Use the principle of elimination of (weakly) dominated strategies to simplify the payoff matrix. What is the optimal solution of the game for the row player? Solve the problem and find an optimal strategy. Clearly indicate your steps.
a b c d e
A | (-2,9) (-1, 7) (7, 10) (9, 7) (0, 10)
B | (3, 7) (2, 6) (4, -10) (5, 5) (0, 8)
C | (4, 6) (-1, 6) (5, 10) (0, -4) (0, 10)
D | (4, -1) (3, 4) (7, 3) (4, 4) (0, -2)
E | (1, 11) (-2, 2) (1, 2) (0, -3) (0, 10)
F | (3, 9) (1, 1) (0, 8) (2, 0) (0, 10)
This was midterm question that I got wrong. I think the correct answer should be
D weakly dominates C
b weakly dominates d
D weakly dominates A, B, E, and F
b weakly dominates a, c, and e
answer = (3, 4)
Can anyone clarify if I'm eliminating correctly?
game-theory
asked Nov 18 '13 at 20:51
zsazsazsusy
143
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up vote
2
down vote
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Below is the payoff matrix of a game. Use the principle of elimination of (weakly) dominated strategies to simplify the payoff matrix. What is the optimal solution of the game for the row player? Solve the problem and find an optimal strategy. Clearly indicate your steps.
a b c d e
A | (-2,9) (-1, 7) (7, 10) (9, 7) (0, 10)
B | (3, 7) (2, 6) (4, -10) (5, 5) (0, 8)
C | (4, 6) (-1, 6) (5, 10) (0, -4) (0, 10)
D | (4, -1) (3, 4) (7, 3) (4, 4) (0, -2)
E | (1, 11) (-2, 2) (1, 2) (0, -3) (0, 10)
F | (3, 9) (1, 1) (0, 8) (2, 0) (0, 10)
This was midterm question that I got wrong. I think the correct answer should be
D weakly dominates C
b weakly dominates d
D weakly dominates A, B, E, and F
b weakly dominates a, c, and e
answer = (3, 4)
Can anyone clarify if I'm eliminating correctly?
game-theory
asked Nov 18 '13 at 20:51
zsazsazsusy
143
1
Welcome to math.SE! Please consider taking the time to read the faq to familiarise yourself with some of our common practices. In addition, this page should give you a start at learning how to typeset mathematics here so that your posts say what you want them to, and also look good. As this question appears to be homework, please consider reading this page for information about asking effective homework-related questions. Cheers!
– user93957
Nov 18 '13 at 21:11
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up vote
2
down vote
favorite
up vote
2
down vote
favorite
Below is the payoff matrix of a game. Use the principle of elimination of (weakly) dominated strategies to simplify the payoff matrix. What is the optimal solution of the game for the row player? Solve the problem and find an optimal strategy. Clearly indicate your steps.
a b c d e
A | (-2,9) (-1, 7) (7, 10) (9, 7) (0, 10)
B | (3, 7) (2, 6) (4, -10) (5, 5) (0, 8)
C | (4, 6) (-1, 6) (5, 10) (0, -4) (0, 10)
D | (4, -1) (3, 4) (7, 3) (4, 4) (0, -2)
E | (1, 11) (-2, 2) (1, 2) (0, -3) (0, 10)
F | (3, 9) (1, 1) (0, 8) (2, 0) (0, 10)
This was midterm question that I got wrong. I think the correct answer should be
D weakly dominates C
b weakly dominates d
D weakly dominates A, B, E, and F
b weakly dominates a, c, and e
answer = (3, 4)
Can anyone clarify if I'm eliminating correctly?
game-theory
asked Nov 18 '13 at 20:51
zsazsazsusy
143
Below is the payoff matrix of a game. Use the principle of elimination of (weakly) dominated strategies to simplify the payoff matrix. What is the optimal solution of the game for the row player? Solve the problem and find an optimal strategy. Clearly indicate your steps.
a b c d e
A | (-2,9) (-1, 7) (7, 10) (9, 7) (0, 10)
B | (3, 7) (2, 6) (4, -10) (5, 5) (0, 8)
C | (4, 6) (-1, 6) (5, 10) (0, -4) (0, 10)
D | (4, -1) (3, 4) (7, 3) (4, 4) (0, -2)
E | (1, 11) (-2, 2) (1, 2) (0, -3) (0, 10)
F | (3, 9) (1, 1) (0, 8) (2, 0) (0, 10)
This was midterm question that I got wrong. I think the correct answer should be
D weakly dominates C
b weakly dominates d
D weakly dominates A, B, E, and F
b weakly dominates a, c, and e
answer = (3, 4)
Can anyone clarify if I'm eliminating correctly?
game-theory
game-theory
asked Nov 18 '13 at 20:51
zsazsazsusy
143
asked Nov 18 '13 at 20:51
zsazsazsusy
143
edited Nov 19 '13 at 2:56
asked Nov 18 '13 at 20:51
zsazsazsusy
143
asked Nov 18 '13 at 20:51
zsazsazsusy
143
asked Nov 18 '13 at 20:51
zsazsazsusy
143
143
1
Welcome to math.SE! Please consider taking the time to read the faq to familiarise yourself with some of our common practices. In addition, this page should give you a start at learning how to typeset mathematics here so that your posts say what you want them to, and also look good. As this question appears to be homework, please consider reading this page for information about asking effective homework-related questions. Cheers!
– user93957
Nov 18 '13 at 21:11
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1
Welcome to math.SE! Please consider taking the time to read the faq to familiarise yourself with some of our common practices. In addition, this page should give you a start at learning how to typeset mathematics here so that your posts say what you want them to, and also look good. As this question appears to be homework, please consider reading this page for information about asking effective homework-related questions. Cheers!
– user93957
Nov 18 '13 at 21:11
1
1
Welcome to math.SE! Please consider taking the time to read the faq to familiarise yourself with some of our common practices. In addition, this page should give you a start at learning how to typeset mathematics here so that your posts say what you want them to, and also look good. As this question appears to be homework, please consider reading this page for information about asking effective homework-related questions. Cheers!
– user93957
Nov 18 '13 at 21:11
Welcome to math.SE! Please consider taking the time to read the faq to familiarise yourself with some of our common practices. In addition, this page should give you a start at learning how to typeset mathematics here so that your posts say what you want them to, and also look good. As this question appears to be homework, please consider reading this page for information about asking effective homework-related questions. Cheers!
– user93957
Nov 18 '13 at 21:11
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1 Answer
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The elimination you did is correct but you have to double check if there is another one. In this case I think there is none but in general with weekly dominated actions, the order you remove them does matter. Important detail: the solution is not $(3,4)$ this is the payoff of the solution. The solution is $(D,b)$.
answered Dec 15 '13 at 7:57
Sergio Parreiras
2,7421332
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1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
The elimination you did is correct but you have to double check if there is another one. In this case I think there is none but in general with weekly dominated actions, the order you remove them does matter. Important detail: the solution is not $(3,4)$ this is the payoff of the solution. The solution is $(D,b)$.
answered Dec 15 '13 at 7:57
Sergio Parreiras
2,7421332
add a comment |Â
up vote
0
down vote
The elimination you did is correct but you have to double check if there is another one. In this case I think there is none but in general with weekly dominated actions, the order you remove them does matter. Important detail: the solution is not $(3,4)$ this is the payoff of the solution. The solution is $(D,b)$.
answered Dec 15 '13 at 7:57
Sergio Parreiras
2,7421332
add a comment |Â
up vote
0
down vote
up vote
0
down vote
The elimination you did is correct but you have to double check if there is another one. In this case I think there is none but in general with weekly dominated actions, the order you remove them does matter. Important detail: the solution is not $(3,4)$ this is the payoff of the solution. The solution is $(D,b)$.
answered Dec 15 '13 at 7:57
Sergio Parreiras
2,7421332
The elimination you did is correct but you have to double check if there is another one. In this case I think there is none but in general with weekly dominated actions, the order you remove them does matter. Important detail: the solution is not $(3,4)$ this is the payoff of the solution. The solution is $(D,b)$.
answered Dec 15 '13 at 7:57
Sergio Parreiras
2,7421332
answered Dec 15 '13 at 7:57
Sergio Parreiras
2,7421332
answered Dec 15 '13 at 7:57
Sergio Parreiras
2,7421332
answered Dec 15 '13 at 7:57
Sergio Parreiras
2,7421332
2,7421332
add a comment |Â
add a comment |Â
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Welcome to math.SE! Please consider taking the time to read the faq to familiarise yourself with some of our common practices. In addition, this page should give you a start at learning how to typeset mathematics here so that your posts say what you want them to, and also look good. As this question appears to be homework, please consider reading this page for information about asking effective homework-related questions. Cheers!
– user93957
Nov 18 '13 at 21:11