Suppose that you and a fellow student are assigned a project on which you will receive one combined grade. You each want to receive a good grade (which means you must work), but you also want to do as little work as possible (which means you shirk). In particular, here is the situation: v If both of you work hard, you both get an A, which gives each of you 40 units of happiness. ' If only one of you works hard, you both get a B, which gives each of you 30 units of happiness. ' If neither of you works hard, you both get a D, which gives each of you 10 units of happiness. (i) Fill in the payoffs in the matrix: (7.5 marks) man- You RE You Classm - : Classma Classmate's _ \"a. Decision ' "am You Classrna'texm - \\ (ii) Assuming your classmate faces the same payoffs and not having any fun will decrease your happiness by 20 units, what is the likely outcome? Explain your answer. (7.5 marks) iii) If you get this person as your partner on a series of projects throughout the year, rather than only once, how might that change the outcome you predicted in part (ii)? (7.5 marks) (iv) Another person on your course cares more about good grades. They get 50 units of happiness for a B and 80 units of happiness for an A. If this person was your partner (but your preferences were unchanged), how would your answers to parts (a) and (b) change? Which of the two partners would you prefer? Would they also want you as a partner? (7.5 marks)