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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...

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.

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