Which are the proper subgames? $($select all that apply$).$

$($the definition of a proper subgame is not on the slides, but I mentioned it in class$).$

Question $1$ options:

The subgame starting at node I

The subgame starting at node II

The subgame starting at node III

The subgame starting at node IV

Question $2(3$ points$)$

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How many strategies does Alice have?

Question $2$ options:

$1$

$2$

$3$

$4$

$5$

$6$

$7$

Question $3(8$ points$)$

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Give all the Nash equilibria of that game $($for each equilibrium, a strategy for Alice and a strategy for Bob$).$

Drawing the normal form version of that game may make things easier.

Question $3$ options:

Question $4(6$ points$)$

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Give all the Subgame Perfect equilibria of that game $($for each equilibrium, a strategy for Alice and a strategy for Bob$).$ For that section we use the following game: