4. [15 points] Consider a game between a home-owner (PI) and a con- tractor (P2). The game has five stages: (i) Pl decides whether to invest an amount / or # on renovating her kitchen, where 0 H - L. (a) Draw the game tree. Find the subgame perfect equilibrium. (b) Is there a hold-up problem in the outcome? Why or why not? Explain what drives the outcome