32. (5 marks) There are two students who are roommates and they dispute over washing the dishes after a party in their unit. Each student's value of a clean kitchen is 100. Each unit of time that passes until the dishes are washed costs each player 1 unit of payoff. Each student 2' chooses the time 33.- 2 0 at which he intends to wash the dishes. The students make their decisions simultaneously by writing their decision t.- on a piece of paper. Student 2' who chooses t1- strictly less than the other student's action tj will wash the dishes. If both students decides to wash the dishes at the same time, then they wash the dishes together and each receives value 50. Payoff of student 2' is given by ti if t;- tj. Find the set of ALL pure strategy Nash equilibria of this game. In equilibrium, who washes the dishes and will there be a delay in washing the dishes? Explain. Show your work and derivation. [Hint: In your answer DRAW the best response correspondence of each player if you find it useful]