Find equilibrium level of s and g in stackelberg equilibrium

Question

Problem

Gilly and Sam are assigned to write a joint paper. Let G denote the time that Gilly spends writing and let S denote the time that Sam spends writing. The grade is determined by the amount of time spent by both. They get utility from a higher grade, but also get utility from leisure. Speci?cally, the utility functions are:

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

Task

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.