Problem 1 Alan and Beatrice have broken the rules and colluded on their quiz, so the Academic Integrity Council is going to interview them. The interviews are taking place simultaneously and there is no communication allowed between the two. The students can either deny or confess to have colluded. The grades without penalty are 65 for Alan and 70 for Beatrice. The Academic Integrity Council has decided on the following scheme: if they both deny they will still be penalized by 20 points respectively. if one denies and the other confesses then the denying student gets zero points while the confessing student retains their original grade, and if they both confess. then they both get a grade of 40. The possible outcomes are summarized in the following table: Beatrice Who are the players in this game? What are their strategies? Use the dot and circle method we went over in class to determine Alan and Beatrice's best responses to the strategies of the other. Do Alan or Beatrice have a dominant strategy? Is there a dominant strategy equilibrium? Based on this information which of the following statements is correct? a. Confessing is the dominated strategy. b. The dominant strategy equilibrium wili result in the highest aggregate grade. c. The Academic Integrity Council has managed to devise a scheme in which the students will definitely confess. d. It is in the interest of the students to deviate from the dominant strategy equilibrium. The following diagram shows Alan's preferences over the possible outcomes when he is completely selfish (red) compared to when he is somewhat altruistic (green). (D. D) - Both deny ; (D. ('l - Alan denies and Beatrice mattresses i D. C) (C. Di - Alan cmtl'esses and Beatrice denies ((2 (7) = Both cmti'ess Bealrice's payoff 0102030 - SO 60 70 80 Alan's payoff Based on this information, which of the following statements is correct? a. When Alan is completely selfish, denying is his dominant strategy. b. When Alan is somewhat altruistic. denying is his dominant strategy. c. When Alan is completely selfish and Beatrice is somewhat altruistic. confessing is Alan's dominant strategy. d. When Alan and Beatrice are both completely selfish. (C. D) is the dominant strategy equilibrium as it is on the highest indifference curve for Alan