Question 3. (24 points) A student stole the DVD player from the student lounge

Question 3. (24 points) A student stole the DVD player from the student lounge. The dean of the 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-collection process is underway but doesn't know whether or not the dean will obtain concrete evidence. The game proceeds as follows: the dean realizes whether or not he has concrete 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: confess (C) or deny (D). Payoffs are realized as follows: if the dean bounces the case, then both players get a payoff of 0. If the dean accuses the student and the student confesses, then the dean gains 2 and the student loses 2. If the dean accuses the student and the student denies, then payoffs depend on whether or not the dean was able to get concrete evidence: if the dean didn't have concrete evidence, then the dean loses 4 and the student gains 4. If, however, the dean was able to get concrete evidence, then he gains 4 and the student loses 4. (a) (10 points) Draw the game tree to describe the game in extensive form. (b) (10 points) Write down the strategic form of the game. (You have to show expected payoff calculation.){c} {if paints] Find all the pure-strategy NE of this game using the payoff matrix in part b above and describe them below using strategies