A professor at the University of Connecticut finds that two students in his class have identical answers on a test. While he does not have any supporting evidence, he is confident that the two students cheated. The professor schedules an appointment so that he can speak with each student separately. He confronts each student with his allegation and offers each student individually the following: Sign a statement admitting to cheating. If both students sign the statement, each will receive an “F” for the course. If only one signs, he is allowed to withdraw from the course while the other student is expelled. If neither sign, both receive a “C” because the professor does not have sufficient evidence to prove cheating.
a) Draw a payoff matrix
b) Which outcome do you expect? Why?
c) What is the Nash Equilibrium in this question?
a) The Payoff matrix for the above game will be drawn as -
b) I expect that the outcome of this game will be that neither of them signing the statement and both receives the 'C' grade. This is because both of them will individually think of Not signing the statement so that they can withdraw from the course, but this will lead to an another outcome which is also good for both of them.
c) The Nash equilibriums of this game as shown in the figure is that both of them signing the statement and getting a 'F' grade.
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