<p>none of the two are methods are really correct.  You do need to use the roll-back logic (or backward induction). However, your tree assumes that Mickey observes Shasha's move, before making a decision instead of choosing simultaneously.  </p>

<p>Weirdly enough, for the game you are given, even though your method is not right, you get to the right solution. The outcome of the unique SPNE is that they both mine gold in year 1. </p>

<p>What you should have done is to find the NE of the second year (mine gold, mine gold) and input that into the cell of the first table in the part that corresponds to (wait, wait). Then solve for the NE of this modified table. </p>

CC BY-SA 4.0
2020-03-16T15:57:32.067Z
2020-03-16T15:57:32.067Z
Regio
<p><a href="https://i.sstatic.net/ksrIK.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ksrIK.png" alt="enter image description here"></a></p>

<p>Is it correct that I have underlined in this matrixes? And therefore the correct answer is (A) ?
Or should I do this like a tree game rollback like this:</p>

<p><a href="https://i.sstatic.net/L33X8.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/L33X8.png" alt="enter image description here"></a></p>

<p>And with the roll back scenario we play like this: </p>

<p><a href="https://i.sstatic.net/x6wxq.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/x6wxq.png" alt="enter image description here"></a></p>

<game-theory>
SPNE in two matrix
soet irl
# SPNE in two matrix

(Asked by: username_0 on 2020-03-16)

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

Is it correct that I have underlined in this matrixes? And therefore the correct answer is (A) ?
Or should I do this like a tree game rollback like this:

[![enter image description here](https://i.sstatic.net/L33X8.png)](https://i.sstatic.net/L33X8.png)

And with the roll back scenario we play like this:

[![enter image description here](https://i.sstatic.net/x6wxq.png)](https://i.sstatic.net/x6wxq.png)

**Tags:** game-theory

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## 1 answers

### Answer by username_1 on 2020-03-16. Score: 1

none of the two are methods are really correct. You do need to use the roll-back logic (or backward induction). However, your tree assumes that Mickey observes Shasha's move, before making a decision instead of choosing simultaneously.

Weirdly enough, for the game you are given, even though your method is not right, you get to the right solution. The outcome of the unique SPNE is that they both mine gold in year 1.

What you should have done is to find the NE of the second year (mine gold, mine gold) and input that into the cell of the first table in the part that corresponds to (wait, wait). Then solve for the NE of this modified table.


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