I have at hand a two period game.
In period 1, Union decides wage offer $w$.
In period 2, firm decides on L, given wage.
Union maximizes $wL$
Firm maximizes $=(L(100-L) - wL) \quad if \quad L<=50 \quad or\quad (2500 - wL) \quad if \quad L>50 $
An SPNE of this game is: w = 50, L = 25.
I need to compute a PO allocation. I know it exsits, but I'm unsure about how to derive it from the payoffs. (Example: w = 40, L = 40. Gives both firm and union strickly greater payoffs.) But, how do I compute the set of PO outcomes from the gives functions? Or even a single PO outcome, without guesswork?