Given the following game:
Find nash equilibrium (NE) Find subgame perfect nash equilibrium.
Main problem i have is with converting this to normal form of the game (because this is i think necessary). I am also not sure about perfect nash equilibrium, but maybe this will be more obvious when i will now the normal form. I am particularly confused with this horizontal dotted line. I would appreciate any help especially with this normal form of this game.
The horizontal dotted line is to suggest that those two nodes are in the same information set. That's to say that P1 cannot tell whether P2 chose A or B. To represent it in the normal form, you need to consider what the strategies are. Remember that a strategy is not an action -- rather, a strategy defines an action for each player at each of his information sets. Therefore, the strategy set for P1 is $S_1=\{ZY,ZX,WY,WX\}$. The strategy set for P2 is $S_2=\{DB,DA,CB,CA\}$.
Then, for the normal form, it's just a matter of working out the payoff for each of strategy profile (that is a strategy for each player). So we get
$$\begin{array}{ccccc} & DB & DA & CB & CA \\ ZY & 3,2 & 3,2 & 6,4 & 6,4 \\ ZX & 3,2 & 3,2 & 6,4 & 6,4 \\ WY & 2,1 & 8,5 & 2,1 & 8,5 \\ WX & 4,6 & 3,0 & 4,6 & 3,0 \end{array}$$
See if you can make any progress from there. Comment if you need further help.