<p>I know that a game has imperfect information if there is an nonsingleton information set, and that defines a situation on which a player can't distinguish between the nodes in the information set. However, I'm wondering if, conceptually, it makes sense that the payoffs <em>can</em> be different, and still the player at the nonsingleton information set can't distinguish between the nodes. For example, consider an extensive form game with imperfect information like the following:</p>
<p><a href="https://i.sstatic.net/1WSBc.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/1WSBc.png" alt="game with a subgame with an infoset with two nodes" /></a></p>
<p>Which appears in <a href="https://www.youtube.com/watch?v=dLWtcWPi84s&amp;ab_channel=GameTheoryOnline" rel="nofollow noreferrer">Game Theory Online</a>. There is an information set with two nodes for player 1 after player 2 choses A or B. Why player 1 can't distinguish at which node she is by the payoffs of, say <span class="math-container">$l$</span>? If she recognizes that the payoff of <span class="math-container">$(0,0)$</span> corresponds for <span class="math-container">$l$</span> after <span class="math-container">$A$</span> and <span class="math-container">$(2,4)$</span> for <span class="math-container">$l$</span> after <span class="math-container">$B$</span>, doesn't this disambiguate the situation?</p>

CC BY-SA 4.0
2021-03-08T06:30:03.373Z
She moves before payoffs are realized, so she cannot use this payoff information.
Michael Greinecker
CC BY-SA 4.0
2021-03-08T08:08:18.077Z
Also, the title is about incomplete information, but the question is about imperfect information.
Michael Greinecker
CC BY-SA 4.0
2021-03-08T12:36:19.247Z
Thanks. And yes, my mistake, I meant "complete and imperfect".
jealcalat
<game-theory><information>
Payoffs in games with imperfect information can be different?
jealcalat
# Payoffs in games with imperfect information can be different?

(Asked by: username_0 on 2021-03-08)

I know that a game has imperfect information if there is an nonsingleton information set, and that defines a situation on which a player can't distinguish between the nodes in the information set. However, I'm wondering if, conceptually, it makes sense that the payoffs *can* be different, and still the player at the nonsingleton information set can't distinguish between the nodes. For example, consider an extensive form game with imperfect information like the following:

[![game with a subgame with an infoset with two nodes](https://i.sstatic.net/1WSBc.png)](https://i.sstatic.net/1WSBc.png)

Which appears in [Game Theory Online](https://www.youtube.com/watch?v=dLWtcWPi84s&ab_channel=GameTheoryOnline). There is an information set with two nodes for player 1 after player 2 choses A or B. Why player 1 can't distinguish at which node she is by the payoffs of, say $l$? If she recognizes that the payoff of $(0,0)$ corresponds for $l$ after $A$ and $(2,4)$ for $l$ after $B$, doesn't this disambiguate the situation?

**Tags:** game-theory, information

> **Comments:**
> **username_1**: She moves before payoffs are realized, so she cannot use this payoff information.  
> **username_1**: Also, the title is about incomplete information, but the question is about imperfect information.  
> **username_0**: Thanks. And yes, my mistake, I meant "complete and imperfect".  

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## 0 answers

