There are n students taking CS 4365. While the students do not talk to each other, they all agree that the course is too difficult. Each student has two options: (1) to tell Vincent that the course is too difficult or (2) to remain silent (and hope that another student will tell him). All the students are interested in telling Vincent that the course is difficult (because they all want an easier final exam). To model this situation, we assume that if any student tells Vincent about this, then all the students get a reward of r. However, it is possible that Vincent would be unhappy about the student who voices people's concern. To model this, whoever decides to talk to Vincent incurs a cost of c. Consequently, if a student decides to talk to Vincent,his/her total payoff is r - c (and the payoff to any other student is r). We assume that c < r.
Also, if none of the students talk to Vincent, they all get a payoff of 0.
Hence, we can model this game as follows. There are n students, each has two pure strategies:
"Tell" or "Ignore". Student i gets the payoff:
• 0 if none of the students tell
• r if one of the students tells
• r - c if i tells
Assuming that the students do not communicate with each other, determine the pure strategy Nash equilibria of the game. Briefly explain your answer.