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