Problem VI: Consider the following dynamic game: An entrant chooses whether to enter the market or stay out. If he chooses to stay out he will get $0, while the incumbent gets $20. If he enters the market, the entrant and the incumbent play the following simultaneous pricing game: they both choose whether to price high or low. If they both price low, they each get $5. If they both price high, they each get $10. If one prices low while the other one prices high, the one who prices low gets $15 and the one who prices high gets $0.

a) Find the sub game perfect nash equilibrium of this game (SPNE=fEnter; Low Low)

b) Find the equilibrium of a modified game where the entrant's outside option is no longer $0, but $10 (SPNE=fStay Out; Low Low)