<p>Consider 
<img src="https://i.sstatic.net/BocOk.png" alt="enter image description here">
where $\epsilon_1,\epsilon_2$ are iid random variables with distribution $F$. $a,b,\dots,h$ are constant parameters.</p>

<p><strong>Game of <em>incomplete but symmetric</em> information</strong>
would be something like: $F$ is common knowledge among the two players. </p>

<p><strong>Game of <em>asymmetric and incomplete</em> information</strong>
would be something like: before making their respective decision, Player 1 observes the realization of $\epsilon_1$ but not $\epsilon_2$ and Player 2 observes $\epsilon_2$ but not $\epsilon_1$.</p>

CC BY-SA 3.0
2015-04-21T23:02:55.293Z
I am not sure, but I think that asymmetric information implies "imperfect information" and not "incomplete information"
Lex
CC BY-SA 3.0
2015-04-21T23:08:54.523Z
@Lex: You're right. I've updated my answer. Thanks for catching the error.
Herr K.
CC BY-SA 3.0
2015-04-21T23:15:03.647Z
Thank you for your reply! Anyway I still have some doubts: in the symmetric case what do the player observe before making their decision? In the asymmetric case is F then not common knowledge?
Lex
CC BY-SA 3.0
2015-04-22T05:11:59.067Z
@Lex: In the symmetric case, you can assume that they don't observe anything before making a decision. In the asymmetric case, it's okay to allow $F$ to be common knowledge; but what's important here is that each player is certain about her own payoff while uncertain about the opponent's payoff, thus making the information structure asymmetric (at the time of making decision).
Herr K.
CC BY-SA 3.0
2015-04-21T22:26:13.427Z
2015-04-21T23:08:25.150Z
2015-04-21T23:08:25.150Z
Herr K.
<p>Verbally:</p>

<p><strong>PERFECT</strong> information: all information available is true (no errors).    </p>

<p><strong>SYMMETRIC</strong> information: all decision-makers involved have exactly the same Information set</p>

<p><strong>COMPLETE</strong> information: the information an agent posses includes all that is known about all aspects of the situation that we examine.  </p>

<p>Note that when examining the information set of a single agent, neither of the above three presupposes or requires the other. 
In some cases though, authors seem to use the word "Complete" in order to mean "we know everything there is to be known" about something, in some "objective" sense. Under this interpretation, it is hard (although not infeasible), to avoid identifying "complete" with "perfect", and this is why I would not suggest this approach, because a clear distinction between "complete" and "perfect" is useful. It is subtle to say (although again, not logically inconsistent) "I know everything there is to know, but some of this knowledge is wrong". It appears better to maintain a "relative" aspect to the concept of "completeness" ("all information <em>available</em>").</p>

CC BY-SA 3.0
2015-05-31T13:44:50.183Z
2015-05-31T13:44:50.183Z
Alecos Papadopoulos
<p>I am having difficulties in distinguish them. I kind of understand what is the difference intuitively, but I still fail to put some games in the correct category.</p>

<p>Can you give me two examples of games and show me the difference from a mathematical (notation) point of view?</p>

<game-theory>
Asymmetric vs incomplete information
Lex
# Asymmetric vs incomplete information

(Asked by: username_0 on 2015-04-21)

I am having difficulties in distinguish them. I kind of understand what is the difference intuitively, but I still fail to put some games in the correct category.

Can you give me two examples of games and show me the difference from a mathematical (notation) point of view?

**Tags:** game-theory


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## 2 answers

### Answer by username_1 on 2015-04-21. Score: 4

Consider
![enter image description here](https://i.sstatic.net/BocOk.png)
where $\epsilon\_1,\epsilon\_2$ are iid random variables with distribution $F$. $a,b,\dots,h$ are constant parameters.

**Game of *incomplete but symmetric* information**
would be something like: $F$ is common knowledge among the two players.

**Game of *asymmetric and incomplete* information**
would be something like: before making their respective decision, Player 1 observes the realization of $\epsilon\_1$ but not $\epsilon\_2$ and Player 2 observes $\epsilon\_2$ but not $\epsilon\_1$.

> **Comments:**
> **username_0**: I am not sure, but I think that asymmetric information implies "imperfect information" and not "incomplete information"  
> **username_1**: @username_0: You're right. I've updated my answer. Thanks for catching the error.  
> **username_0**: Thank you for your reply! Anyway I still have some doubts: in the symmetric case what do the player observe before making their decision? In the asymmetric case is F then not common knowledge?  
> **username_1**: @username_0: In the symmetric case, you can assume that they don't observe anything before making a decision. In the asymmetric case, it's okay to allow $F$ to be common knowledge; but what's important here is that each player is certain about her own payoff while uncertain about the opponent's payoff, thus making the information structure asymmetric (at the time of making decision).  

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### Answer by username_2 on 2015-05-31. Score: 1

Verbally:

**PERFECT** information: all information available is true (no errors).

**SYMMETRIC** information: all decision-makers involved have exactly the same Information set

**COMPLETE** information: the information an agent posses includes all that is known about all aspects of the situation that we examine.

Note that when examining the information set of a single agent, neither of the above three presupposes or requires the other.
In some cases though, authors seem to use the word "Complete" in order to mean "we know everything there is to be known" about something, in some "objective" sense. Under this interpretation, it is hard (although not infeasible), to avoid identifying "complete" with "perfect", and this is why I would not suggest this approach, because a clear distinction between "complete" and "perfect" is useful. It is subtle to say (although again, not logically inconsistent) "I know everything there is to know, but some of this knowledge is wrong". It appears better to maintain a "relative" aspect to the concept of "completeness" ("all information *available*").


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