Million DS Satellite: 3-way bubble strategy

[Shadowlike]

So I just played a double shootout to the million that paid 2 seats.

This was the first time I was faced with this situation which I found very interesting, so I'd like to know if I made the right decisions.

3 way, the situation was initially as follows:
Seat 1: me (2k chips)
Seat 2: 4k chips
Seat 3: 9k
Blinds were 50/100, later 75/150.

Big Stack was raising 50% of his button (to 4BB), so I was 1st to act 50% in my SB. In my BB, i was faced either with a push of S2 or a 4BB raise of S3, no walks for me.

-Should I play any flops or is it better to pushbot? (I decided not to play any flops).
-What are my optimal ranges? In what situations should I push loose/tight?

After some time, I managed to double up vs bigstack S3 by pushing AQ in my SB to his A8 Button raise.
The stacks were then:
Seat 1: me (4k chips)
Seat 2: 4k
Seat 3: 7k

-How does my optimal strategy change?

Also, is there some kind of mathematical theory for this simple kind of situation? Seems like the theory of Nash equilibra could be applicable?!