Mixing
Closure of the graphic of the vector of the players' payoff functions
Let $X_i$ be a compact subset of a topological vector space (not necessarily Hausdorff) , $i=1,ldots,N$,
$ u_i: Xrightarrow mathbb{R}$ the payoff functions and $u$ the vector of the players' payoff functions.
Is true that the closure of the graphic of $u$ is a subset of $Xtimes mathbb{R}^N$?
game-theory
asked Nov 20 '18 at 6:54
Diego Cornejo Koc
63
|
show 4 more comments
Let $X_i$ be a compact subset of a topological vector space (not necessarily Hausdorff) , $i=1,ldots,N$,
$ u_i: Xrightarrow mathbb{R}$ the payoff functions and $u$ the vector of the players' payoff functions.
Is true that the closure of the graphic of $u$ is a subset of $Xtimes mathbb{R}^N$?
game-theory
asked Nov 20 '18 at 6:54
Diego Cornejo Koc
63
It's the graph, not graphic. And yes.
– Michael Greinecker♦
Nov 20 '18 at 7:22
I'm sorry because of that. Can you give me a hint?
– Diego Cornejo Koc
Nov 20 '18 at 13:14
This is pretty much a direct consequence of the definition of the graph of a function, see en.wikipedia.org/wiki/Graph_of_a_function
– Michael Greinecker♦
Nov 20 '18 at 13:39
But $overline{Gr(u)} subseteq overline{Xtimes mathbb{R}^N} = overline{X}times mathbb{R}^N$ and $X$ is not necessarily closed.
– Diego Cornejo Koc
Nov 20 '18 at 13:50
$X$ is compact as the Cartesian product of compact spaces.
– Michael Greinecker♦
Nov 20 '18 at 14:06
|
show 4 more comments
Let $X_i$ be a compact subset of a topological vector space (not necessarily Hausdorff) , $i=1,ldots,N$,
$ u_i: Xrightarrow mathbb{R}$ the payoff functions and $u$ the vector of the players' payoff functions.
Is true that the closure of the graphic of $u$ is a subset of $Xtimes mathbb{R}^N$?
game-theory
asked Nov 20 '18 at 6:54
Diego Cornejo Koc
63
Let $X_i$ be a compact subset of a topological vector space (not necessarily Hausdorff) , $i=1,ldots,N$,
$ u_i: Xrightarrow mathbb{R}$ the payoff functions and $u$ the vector of the players' payoff functions.
Is true that the closure of the graphic of $u$ is a subset of $Xtimes mathbb{R}^N$?
game-theory
game-theory
asked Nov 20 '18 at 6:54
Diego Cornejo Koc
63
asked Nov 20 '18 at 6:54
Diego Cornejo Koc
63
asked Nov 20 '18 at 6:54
Diego Cornejo Koc
63
asked Nov 20 '18 at 6:54
Diego Cornejo Koc
63
asked Nov 20 '18 at 6:54
Diego Cornejo Koc
63
63
It's the graph, not graphic. And yes.
– Michael Greinecker♦
Nov 20 '18 at 7:22
I'm sorry because of that. Can you give me a hint?
– Diego Cornejo Koc
Nov 20 '18 at 13:14
This is pretty much a direct consequence of the definition of the graph of a function, see en.wikipedia.org/wiki/Graph_of_a_function
– Michael Greinecker♦
Nov 20 '18 at 13:39
But $overline{Gr(u)} subseteq overline{Xtimes mathbb{R}^N} = overline{X}times mathbb{R}^N$ and $X$ is not necessarily closed.
– Diego Cornejo Koc
Nov 20 '18 at 13:50
$X$ is compact as the Cartesian product of compact spaces.
– Michael Greinecker♦
Nov 20 '18 at 14:06
|
show 4 more comments
It's the graph, not graphic. And yes.
– Michael Greinecker♦
Nov 20 '18 at 7:22
I'm sorry because of that. Can you give me a hint?
– Diego Cornejo Koc
Nov 20 '18 at 13:14
This is pretty much a direct consequence of the definition of the graph of a function, see en.wikipedia.org/wiki/Graph_of_a_function
– Michael Greinecker♦
Nov 20 '18 at 13:39
But $overline{Gr(u)} subseteq overline{Xtimes mathbb{R}^N} = overline{X}times mathbb{R}^N$ and $X$ is not necessarily closed.
– Diego Cornejo Koc
Nov 20 '18 at 13:50
$X$ is compact as the Cartesian product of compact spaces.
– Michael Greinecker♦
Nov 20 '18 at 14:06
It's the graph, not graphic. And yes.
– Michael Greinecker♦
Nov 20 '18 at 7:22
It's the graph, not graphic. And yes.
– Michael Greinecker♦
Nov 20 '18 at 7:22
I'm sorry because of that. Can you give me a hint?
– Diego Cornejo Koc
Nov 20 '18 at 13:14
I'm sorry because of that. Can you give me a hint?
– Diego Cornejo Koc
Nov 20 '18 at 13:14
This is pretty much a direct consequence of the definition of the graph of a function, see en.wikipedia.org/wiki/Graph_of_a_function
– Michael Greinecker♦
Nov 20 '18 at 13:39
This is pretty much a direct consequence of the definition of the graph of a function, see en.wikipedia.org/wiki/Graph_of_a_function
– Michael Greinecker♦
Nov 20 '18 at 13:39
But $overline{Gr(u)} subseteq overline{Xtimes mathbb{R}^N} = overline{X}times mathbb{R}^N$ and $X$ is not necessarily closed.
– Diego Cornejo Koc
Nov 20 '18 at 13:50
But $overline{Gr(u)} subseteq overline{Xtimes mathbb{R}^N} = overline{X}times mathbb{R}^N$ and $X$ is not necessarily closed.
– Diego Cornejo Koc
Nov 20 '18 at 13:50
$X$ is compact as the Cartesian product of compact spaces.
– Michael Greinecker♦
Nov 20 '18 at 14:06
$X$ is compact as the Cartesian product of compact spaces.
– Michael Greinecker♦
Nov 20 '18 at 14:06
|
show 4 more comments
active
oldest
votes
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%2f3006033%2fclosure-of-the-graphic-of-the-vector-of-the-players-payoff-functions%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3006033%2fclosure-of-the-graphic-of-the-vector-of-the-players-payoff-functions%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
It's the graph, not graphic. And yes.
– Michael Greinecker♦
Nov 20 '18 at 7:22
I'm sorry because of that. Can you give me a hint?
– Diego Cornejo Koc
Nov 20 '18 at 13:14
This is pretty much a direct consequence of the definition of the graph of a function, see en.wikipedia.org/wiki/Graph_of_a_function
– Michael Greinecker♦
Nov 20 '18 at 13:39
But $overline{Gr(u)} subseteq overline{Xtimes mathbb{R}^N} = overline{X}times mathbb{R}^N$ and $X$ is not necessarily closed.
– Diego Cornejo Koc
Nov 20 '18 at 13:50
$X$ is compact as the Cartesian product of compact spaces.
– Michael Greinecker♦
Nov 20 '18 at 14:06