Project: FINAL EXAM:
This game is played by three players: The teacher, student X
and student Y. Of course, there are also 20 other students, but they don't make decisions
and therefore do not really participate in the game.
Student X makes the first move by wearing his cap to class or not.
Seeing this, Student Y has the same option, cap or not.
Seeing the two students with or without caps,
the teacher makes the decision to have a special eye (a) on X,
or (b) on Y, or (c) the teacher could also relax. Seeing the teacher react, each one of students X and Y
decides for himself whether to cheat or not.
Cheating, when not noticed by the teacher, brings a better grade, a payoff of 1.
If the teacher notices cheating, disciplinary measures are taken, a payoff of -6 for the student.
Cheating is noticed by the teacher
- with probability 1/5 if the student has no cap to hide and the teacher has no special eye on the student,
- with probability 1/10 if the student wears a cap but the teacher has no special eye on the student,
- with probability 1/3 if the student wears no cap and the teacher has a special eye on the student,
- with probability 1/6 if the student wears a cap and the teacher has a special eye on the student.
The teacher has also payoffs. It is the sum of a value of -1 if he or she has to keep an eye on a student,
compared to 0 if he or she can relax, and a value of -2 if cheating has occurred but gone unnoticed.
How will the players play? Modify the model if you deem it necessary.