Reduce the payoff matrix using (weakly) dominated strategies
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
add a comment |
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
add a comment |
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
add a comment |
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
add a comment |
1 Answer
1
active
oldest
votes
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
2,75711332
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f572368%2freduce-the-payoff-matrix-using-weakly-dominated-strategies%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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
2,75711332
add a comment |
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
2,75711332
add a comment |
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
2,75711332
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
2,75711332
answered Dec 15 '13 at 7:57
Sergio Parreiras
2,75711332
answered Dec 15 '13 at 7:57
Sergio Parreiras
2,75711332
answered Dec 15 '13 at 7:57
Sergio Parreiras
2,75711332
2,75711332
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f572368%2freduce-the-payoff-matrix-using-weakly-dominated-strategies%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
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