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HmWk03_Ans

# HmWk03_Ans - Economics 1200 Spring 2012 Answers to Homework...

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1 Economics 1200 Spring 2012 Answers to Homework # 3 1. (a) The game in normal form can be depicted using two payoff tables. Payoffs are net of contribution costs, and are in the order: Larry, Curly, Moe. Larry’s Choice Moe Chooses Contribute Larry’s Choice Moe Chooses Not Contribute Curly’s Choice Curly’s Choice Contribute Don’t Contribute Contribute Don’t Contribute Contribute 1.5, 1.5, 1.5 0.5, 2.0, 0.5 Contribute 0.5, 0.5, 2.0 -0.5, 1.0, 1.0 Don’t Contribute 2.0, 0.5, 0.5 1.0, 1.0, -0.5 Don’t Contribute 1.0, -0.5, 1.0 0.0, 0.0, 0.0 (b) The unique Nash equilibrium, found using best response analysis is: (Don’t Contribute, Don’t Contribute, Don’t Contribute). The strategy don’t contribute is dominant for all three players. This is a generalization of the prisoner’s dilemma game, called a social dilemma (in groups greater than 2). 2. (a) The event A consists of the six outcomes (1,6), (2,5), (3,4), (4,3), (5,2),(6,1) where the first (second) element is the number on the red (white) die. Since the sample space, S, from rolling two dice has 6x6=36 possible outcomes, it follows that P(A)=6/36 =1/6. The event B also has six possibilities: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), so P(B)=6/36=1/6. (b) By the addition rule, P(A B)=P(A)+P(B)-P(A B). P(A B) is not empty as can be seen from the descriptions above of the possible outcomes for the two events. In particular, (1,6) is an outcome that satisfies both event A and B. Since (1,6) is just one of 36 possible outcomes from rolling two dice, P(A B) = 1/36. It follows that: P(A B) = 1/6 + 1/6 -1/36 = 11/36. 3. Let B=boy, G=girl. The sample space for this problem, S={(B,B),(G,B),(B,G),(G,G)}, where the first (second) element refers to the first (second) -born child. Define A=”one child is a girl” and the event B=”one child is the king,” We want to find the conditional probability, P(A|B)=P(A B)/P(B). Assuming a king is a boy, P(B)=3/4=P(A), which follows from the sample space S. What is P(A B)? The only

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