If you draw the corresponding game tree, you will see that "equivalent to simultaneous move game" implies that the game has no proper subgame and the only subgame is the whole game.
This is because the information set of the second player covers every move of the first player.
Therefore, every Nash equilibrium is trivially also subgame perfect.
The two (pure) Nash equilibrium in this game is (Betray, Silent) and (Silent, Betray).
Let us see why (Betray, Silent) is an equilibrium.
Let us look at person A.
Person B is playing Silent.
If she plays Betray, she gets $2$.
If she deviates to Silent, she gets $1$. So she would not play Silent.
Now consider person B.
Person A is playing Betray.
If she ...
The trick for finding a mixed strategy Nash Equilibrium is that given everyone else's strategies, all players will be indifferent between each of the options their randomizing over (ie. those options will yield the same payoff). So all you need to do is write an expression relating each player's expected payoffs for each strategy, and solve for the ...