Thank you!

3. Game Theory. Two roommates each need to choose to clean their apartment, and each can choose any amount of time ti 2 0 to clean. If their choices are t,- and tj, then player #5 payoff is given by (10 tj)t3' 133.1 (This payo function implies that the more one roommate cleans, the less valuable is cleaning for the other roommate). (a) Find a NE pair of cleaning times, ($1,152). (b) Now suppose that P1 gets to choose her cleaning time t1 rst, then P2 sees and responds to this with his choice 132. What are the (SPNE) cleaning times