game theory-Are second priced bids always a nash equilibrium?
$begingroup$
I'm trying to understand the basics of game theory and the topic of auctions have come up. What I want to know is second priced bids always a nash equilibrium?
Suppose we have this question.
We consider a second price sealed-bid auction with complete information. We have n bidders,
n ≥ 2. There is only one object in the auction. Player i, i = 1, . . . , n, evaluates the object by
giving it a valuation vi
, where:
v1 > v2 > v3 > . . . > vn > 0
Each player i submits a sealed bid bi
, i = 1, . . . , n. So, we can describe a bidding profile of all
players as (b1, b2, b3, . . . , bn).
A) Is the bidding profile (v1, v2, v3, . . . , vn), i.e., the one where every player bids her
valuation of the item, a Nash equilibrium of the game?
B) Is the bidding profile (v1, 0, 0, . . . , 0) a Nash equilibrium of the game?
C) Is the bidding profile (v2, v1, 0, . . . , 0) a Nash equilibrium of the game?
Surely it's always a nash equilibrium becuase every bidder will bid there valuation for the item thus no one has any incentive to change there bid? E.G a weakly dominant strategy
I just wanted some clarification on questions A, B and C as I thought they would all have nash equilibrium regardless.
Question has been solved this can now be closed.
game-theory nash-equilibrium auction-theory
asked Jan 15 at 21:21
SearchingForSearchingFor
918
$endgroup$
add a comment |
$begingroup$
I'm trying to understand the basics of game theory and the topic of auctions have come up. What I want to know is second priced bids always a nash equilibrium?
Suppose we have this question.
We consider a second price sealed-bid auction with complete information. We have n bidders,
n ≥ 2. There is only one object in the auction. Player i, i = 1, . . . , n, evaluates the object by
giving it a valuation vi
, where:
v1 > v2 > v3 > . . . > vn > 0
Each player i submits a sealed bid bi
, i = 1, . . . , n. So, we can describe a bidding profile of all
players as (b1, b2, b3, . . . , bn).
A) Is the bidding profile (v1, v2, v3, . . . , vn), i.e., the one where every player bids her
valuation of the item, a Nash equilibrium of the game?
B) Is the bidding profile (v1, 0, 0, . . . , 0) a Nash equilibrium of the game?
C) Is the bidding profile (v2, v1, 0, . . . , 0) a Nash equilibrium of the game?
Surely it's always a nash equilibrium becuase every bidder will bid there valuation for the item thus no one has any incentive to change there bid? E.G a weakly dominant strategy
I just wanted some clarification on questions A, B and C as I thought they would all have nash equilibrium regardless.
Question has been solved this can now be closed.
game-theory nash-equilibrium auction-theory
asked Jan 15 at 21:21
SearchingForSearchingFor
918
$endgroup$
add a comment |
$begingroup$
I'm trying to understand the basics of game theory and the topic of auctions have come up. What I want to know is second priced bids always a nash equilibrium?
Suppose we have this question.
We consider a second price sealed-bid auction with complete information. We have n bidders,
n ≥ 2. There is only one object in the auction. Player i, i = 1, . . . , n, evaluates the object by
giving it a valuation vi
, where:
v1 > v2 > v3 > . . . > vn > 0
Each player i submits a sealed bid bi
, i = 1, . . . , n. So, we can describe a bidding profile of all
players as (b1, b2, b3, . . . , bn).
A) Is the bidding profile (v1, v2, v3, . . . , vn), i.e., the one where every player bids her
valuation of the item, a Nash equilibrium of the game?
B) Is the bidding profile (v1, 0, 0, . . . , 0) a Nash equilibrium of the game?
C) Is the bidding profile (v2, v1, 0, . . . , 0) a Nash equilibrium of the game?
Surely it's always a nash equilibrium becuase every bidder will bid there valuation for the item thus no one has any incentive to change there bid? E.G a weakly dominant strategy
I just wanted some clarification on questions A, B and C as I thought they would all have nash equilibrium regardless.
Question has been solved this can now be closed.
game-theory nash-equilibrium auction-theory
asked Jan 15 at 21:21
SearchingForSearchingFor
918
$endgroup$
I'm trying to understand the basics of game theory and the topic of auctions have come up. What I want to know is second priced bids always a nash equilibrium?
Suppose we have this question.
We consider a second price sealed-bid auction with complete information. We have n bidders,
n ≥ 2. There is only one object in the auction. Player i, i = 1, . . . , n, evaluates the object by
giving it a valuation vi
, where:
v1 > v2 > v3 > . . . > vn > 0
Each player i submits a sealed bid bi
, i = 1, . . . , n. So, we can describe a bidding profile of all
players as (b1, b2, b3, . . . , bn).
A) Is the bidding profile (v1, v2, v3, . . . , vn), i.e., the one where every player bids her
valuation of the item, a Nash equilibrium of the game?
B) Is the bidding profile (v1, 0, 0, . . . , 0) a Nash equilibrium of the game?
C) Is the bidding profile (v2, v1, 0, . . . , 0) a Nash equilibrium of the game?
Surely it's always a nash equilibrium becuase every bidder will bid there valuation for the item thus no one has any incentive to change there bid? E.G a weakly dominant strategy
I just wanted some clarification on questions A, B and C as I thought they would all have nash equilibrium regardless.
Question has been solved this can now be closed.
game-theory nash-equilibrium auction-theory
game-theory nash-equilibrium auction-theory
asked Jan 15 at 21:21
SearchingForSearchingFor
918
asked Jan 15 at 21:21
SearchingForSearchingFor
918
edited Jan 23 at 18:03
SearchingFor
asked Jan 15 at 21:21
SearchingForSearchingFor
918
asked Jan 15 at 21:21
SearchingForSearchingFor
918
asked Jan 15 at 21:21
SearchingForSearchingFor
918
918
add a comment |
add a comment |
0
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%2f3074985%2fgame-theory-are-second-priced-bids-always-a-nash-equilibrium%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
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.
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%2f3074985%2fgame-theory-are-second-priced-bids-always-a-nash-equilibrium%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
