1. Alan and Beatrice are students who are suspected of colluding on their assignment. The examiners are going to interview each of them individually, in separate rooms. Alan and Beatrice must each choose whether to Deny or Confess. The following diagram shows Alan's preferences over the possible outcomes when he is completely selfish (red, vertical lines) compared to when he is somewhat altruistic (green curves). Based on this information, determine whether each of the following statements is true or false. 80- (D, C) 70- 60- Beatrice's payoff 50 40- 30- 20 10 0 0 10 (D.D) - Both deny (D, C)-Alan denies and Beatrice confesses (C, D)-Alan confesses and Beatrice denies (CC)-Both confess (C,C) (D.D) (C,D) 20 30 40 50 60 70 80 Alan's payoff (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.
1. Alan and Beatrice are students who are suspected of colluding on their assignment. The examiners are going to interview each of them individually, in separate rooms. Alan and Beatrice must each choose whether to Deny or Confess. The following diagram shows Alan's preferences over the possible outcomes when he is completely selfish (red, vertical lines) compared to when he is somewhat altruistic (green curves). Based on this information, determine whether each of the following statements is true or false. 80- (D, C) 70- 60- Beatrice's payoff 50 40- 30- 20 10 0 0 10 (D.D) - Both deny (D, C)-Alan denies and Beatrice confesses (C, D)-Alan confesses and Beatrice denies (CC)-Both confess (C,C) (D.D) (C,D) 20 30 40 50 60 70 80 Alan's payoff (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.
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.9P
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![1. Alan and Beatrice are students who are suspected of colluding on their assignment. The
examiners are going to interview each of them individually, in separate rooms. Alan and Beatrice
must each choose whether to Deny or Confess. The following diagram shows Alan's preferences
over the possible outcomes when he is completely selfish (red, vertical lines) compared to when he
is somewhat altruistic (green curves). Based on this information, determine whether each of the
following statements is true or false.
80-
(D, C)
70-
Beatrice's payoff
60-
50
40-
30
20
10-
1
0 10
(D, D) Both deny
(D, C) = Alan denies and Beatrice confesses
(C, D) - Alan confesses and Beatrice denies
(C, C)= Both confess
1
1
(C, C)
(D. D)
20 30 40 50
Alan's payoff
(C, D) -
60 70 80
(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F35bc7cfb-e38c-45d6-8cb2-8c987ddfb016%2F00b25066-000a-43b0-8b75-3c2b8808bd61%2Ffco7bwl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Alan and Beatrice are students who are suspected of colluding on their assignment. The
examiners are going to interview each of them individually, in separate rooms. Alan and Beatrice
must each choose whether to Deny or Confess. The following diagram shows Alan's preferences
over the possible outcomes when he is completely selfish (red, vertical lines) compared to when he
is somewhat altruistic (green curves). Based on this information, determine whether each of the
following statements is true or false.
80-
(D, C)
70-
Beatrice's payoff
60-
50
40-
30
20
10-
1
0 10
(D, D) Both deny
(D, C) = Alan denies and Beatrice confesses
(C, D) - Alan confesses and Beatrice denies
(C, C)= Both confess
1
1
(C, C)
(D. D)
20 30 40 50
Alan's payoff
(C, D) -
60 70 80
(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.
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