Gilly and Sam are assigned to write 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)

question:

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.