Gilly and Sam are assigned to do a joint paper. Let G denote the time thatGilly spends writing and let S denote the time that Sam spends writing. The grade is determinedby the amount of time spent by both. They get utility from a higher grade, but also get utility fromleisure. Specically, the utility functions are:

U^Gilly= ln(G+S) + ln(18-G)

U^Sam= ln(S+G) + ln(18-S)

1. Find the Nash equilibrium levels of G and S if they move simultaneously.

2. What levels of G and S would have maximized their total utility, TU=UGilly+USam ?

3. Now assume that Gilly and Sam decide to move sequentially. Sam wins the coin toss and decides his time S rst. After observing S, Gilly then decides her time G. Find the equilibrium levels of S and G in the Stackelberg equilibrium