# The Dean’s Dilemma: A student stole the DVD player from the student lounge. The dean of students (player 1) suspects the student (player 2) and…

The Dean’s Dilemma: A student stole the DVD player from the student

lounge. The dean of students (player 1) suspects the student (player 2) and

begins collecting evidence. However, evidence collection is a random process,

and concrete evidence will be available to the dean only with probability 1

2 .

The student knows that the evidence-gathering process is under way but does

not know whether the dean has collected evidence or not. The game proceeds

as follows: The dean realizes whether or not he has evidence and can then

choose his action, whether to accuse the student (A) or bounce the case (B) and forget it. Once accused, the student has two options: he can either confess (C)or deny (D). Payoffs are realized as follows: If the dean bounces the case thenboth players get 0. If the dean accuses the student and the student confesses,the dean gains 2 and the student loses 2. If the dean accuses the student andthe student denies, then payoffs depend on the evidence: If the dean has noevidence then he loses face, which gives him a loss of 4, while the studentgains glory, which gives him a payoff of 4. If, however, the dean has evidencethen he is triumphant and gains 4, while the student is put on probation andloses 4.a. Draw the game tree that represents the extensive form of this game.b. Write down the matrix that represents the normal form of the extensiveform you drew in (a).c. Solve for the Nash equilibria of the game.