Real Bonus Points - If everyone chooses collude, all students get 10 bonus points in the final exam. - If everyone chooses to collude, but one person defects, that person gets 50 bonus points in the nal exam, and no other student gets any points. - If more than 1 person chooses to defect, no student receives any bonus points. (a) Find the payoff matrix assuming that there are only two players: You and Your classmate. Collude Collude You Defect (b) Find the payoff matrix assuming that there are (N + 1) players: You and N classmates, where N > 1. That is, you play the game with at least two classmates. N classmates All N classmates At least one of N Collude classmates Defect (c) In part (a), do you have a dominant strategy? Explain. (d) In part (b), do you have a dominant strategy? Does this answer depend on whether there is more than one classmate who chooses Defect (e. g, two classmates choose Defect)? Explain. (e) Based on your answers to part (c) and (d), which choice should you make if your objective is to maximize payoff? What choice did you actually make in the games in class? Explain. (i) What have you learned from playing the game? Explain.