Yara and Theon are assigned to work on a joint project in the next 6 hours. Let Y denote the time that Yarra spend working and T be the time that Theon spend working. The grade is determined by the amount of time spent by both. They get utility from higher grade and also from leisure

U (Yarra) = ln(Y+T) + ln ( 6-Y)

U(Theon) = ln(Y+T) + ln( 6-T)

A) FIND NASH EQUILIBRIUM LEVELS OF Y AND T IF THEY MOVE SIMUTANOUESLY

B) ASSUM YARRA AND THEON DECIDE TO MOVE SEQUENTIALLY. YARRA WINS COIN TOSS AND DECIDE HER TIME Y FIRST. AFTER OBSERVING Y, THEON DECIDES HIS TIME T. FIND THE OPTIMAL LEVEL OF Y AND T