<p>It is well-known that the first-price auction is <em>manipulable</em>, in that a player can improve his utility by bidding less than his true value. But successful manipulation requires information: the player should know the maximum bid of the other players. Otherwise, he might bid too low and lose the auction.</p>
<p>Other mechanisms require less information. For example, consider the <em>average mechanism</em> on a one-dimensional domain (each agent bids his ideal value, and the outcome is the average of all bids). Here, in order to bid successfully, a player only needs to know whether the average of the other players is higher or lower than his true value: if it is higher, he should bid the minimum value; if it is lower, he should bid the maximum value. So only a single bit of information is required, and one can say that this mechanism is easier to manipulate.</p>
<p>QUESTION: are there studies about the amount of information needed to manipulate various mechanisms?</p>

CC BY-SA 4.0
2023-08-29T23:23:34.727Z
In what sense does the average contain less information than the maximum?
Herr K.
CC BY-SA 4.0
2023-08-29T23:55:41.587Z
The proposed manipulation of the average mechanism doesn't always work. If the average is very, very close to your optimum, the strategy might overcorrect and make things worse.
Michael Greinecker
CC BY-SA 4.0
2023-08-30T02:11:33.267Z
@HerrK. You do not need to know the exact average - only whether it is higher or lower than your value (one bit of information).
Erel Segal-Halevi
CC BY-SA 4.0
2023-08-30T11:24:58.340Z
@MichaelGreinecker you are right - this is not a very good example.
Erel Segal-Halevi
<game-theory><mechanism-design>
How much information is required to manipulate a mechanism?
Erel Segal-Halevi
# How much information is required to manipulate a mechanism?

(Asked by: username_0 on 2023-08-29)

It is well-known that the first-price auction is *manipulable*, in that a player can improve his utility by bidding less than his true value. But successful manipulation requires information: the player should know the maximum bid of the other players. Otherwise, he might bid too low and lose the auction.

Other mechanisms require less information. For example, consider the *average mechanism* on a one-dimensional domain (each agent bids his ideal value, and the outcome is the average of all bids). Here, in order to bid successfully, a player only needs to know whether the average of the other players is higher or lower than his true value: if it is higher, he should bid the minimum value; if it is lower, he should bid the maximum value. So only a single bit of information is required, and one can say that this mechanism is easier to manipulate.

QUESTION: are there studies about the amount of information needed to manipulate various mechanisms?

**Tags:** game-theory, mechanism-design

> **Comments:**
> **username_1**: In what sense does the average contain less information than the maximum?  
> **username_2**: The proposed manipulation of the average mechanism doesn't always work. If the average is very, very close to your optimum, the strategy might overcorrect and make things worse.  
> **username_0**: @HerrK. You do not need to know the exact average - only whether it is higher or lower than your value (one bit of information).  
> **username_0**: @MichaelGreinecker you are right - this is not a very good example.  

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## 0 answers

