<p>Thanks to denesp, I realised that I was only considering outcomes resulting from the following subgame:</p>

<p><img src="https://i.sstatic.net/zYatG.jpg" alt="enter image description here"></p>

<p>If you consider all outcomes within the extensive form, then it is clear that $(2,6)$ pareto dominates $(0,5)$.</p>

CC BY-SA 3.0
2015-04-21T22:23:51.553Z
2015-04-21T22:34:04.993Z
2015-04-21T22:34:04.993Z
Five σ
<p><img src="https://i.sstatic.net/ept0F.jpg" alt="enter image description here"></p>

<p>The question I'm dealing with is:</p>

<blockquote>
  <p>Suppose A plays <em>bf</em>, Which of B's strategies would lead to an outcome that is not pareto efficient?</p>
</blockquote>

<p>The answer is apparently <em>ei</em> as $(bf,ei)=(0,5)$, but I don't understand why. If this answer is correct, could you please explain why?</p>

<p>My understanding of pareto efficiency is that by moving from $(x,y)$, we cannot make any player better off without making the other worse off. If this is the case, then $(x,y)$ is pareto efficient.</p>

<p>$(x,y)$ would be pareto inefficient if there exists a movement away from $(x,y)$, where a player can be made better off without the other being made worse off.</p>

<p>From $(bf,ei)=(0,5)$, we can move to:</p>

<p>$(4,4), (5,0),(2,2)$</p>

<p>I don't see how we can move to any of these without making B worse off, I think that $(bf,ei)$ represents a pareto efficient outcome.</p>

<p>Any chance you could offer some advice?</p>

<p>Thanks.</p>

CC BY-SA 3.0
2015-04-21T22:03:06.263Z
If A would play $(af)$ while B maintained $(ei)$ the outcome would be (2,6), which Pareto dominates (0,5).
Giskard
CC BY-SA 3.0
2015-04-21T22:19:39.300Z
Ah, thank you. I was only considering the outcomes from the subgame initiated after B plays e. If you want to rewrite your comment as an answer, I'd be happy to accept it.
Five σ
CC BY-SA 3.0
2015-04-22T05:26:47.047Z
Thank you, but I am content with your answer.
Giskard
<game-theory>
Extensive form: pareto inefficiency?
Five σ
# Extensive form: pareto inefficiency?

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

![enter image description here](https://i.sstatic.net/ept0F.jpg)

The question I'm dealing with is:

> Suppose A plays *bf*, Which of B's strategies would lead to an outcome that is not pareto efficient?

The answer is apparently *ei* as $(bf,ei)=(0,5)$, but I don't understand why. If this answer is correct, could you please explain why?

My understanding of pareto efficiency is that by moving from $(x,y)$, we cannot make any player better off without making the other worse off. If this is the case, then $(x,y)$ is pareto efficient.

$(x,y)$ would be pareto inefficient if there exists a movement away from $(x,y)$, where a player can be made better off without the other being made worse off.

From $(bf,ei)=(0,5)$, we can move to:

$(4,4), (5,0),(2,2)$

I don't see how we can move to any of these without making B worse off, I think that $(bf,ei)$ represents a pareto efficient outcome.

Any chance you could offer some advice?

Thanks.

**Tags:** game-theory

> **Comments:**
> **username_1**: If A would play $(af)$ while B maintained $(ei)$ the outcome would be (2,6), which Pareto dominates (0,5).  
> **username_0**: Ah, thank you. I was only considering the outcomes from the subgame initiated after B plays e. If you want to rewrite your comment as an answer, I'd be happy to accept it.  
> **username_1**: Thank you, but I am content with your answer.  

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## 1 answers

### Answer by username_0 on 2015-04-21. Score: 3 | Accepted answer

Thanks to denesp, I realised that I was only considering outcomes resulting from the following subgame:

![enter image description here](https://i.sstatic.net/zYatG.jpg)

If you consider all outcomes within the extensive form, then it is clear that $(2,6)$ pareto dominates $(0,5)$.


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