Simon Fraser University
Spring 2016
Econ 302 Assignment 2
Due: in Lecture, Tuesday January 26, 2016.
Show all your work.
1.
(4 points) For each of the following games, (i) find strategies that survive iterative
deletion of strictly dominated strategies (ISD), and (ii) find all Nash equilibria (both pure
and mixed). For each strategy that you delete, you must write down the strategy that strictly
dominates it.
a.
T
M
B
L
C
R
4,0 2,1 3,2
2,2 3,4 0,1
2,3 1,2 0,3
X
Y
Z
A 1,2 1,2 0,3
b. B 4,0 1,3 0,2
C 3,1 2,1 1,2
D 0,2 0,1 2,4
X
A 7,2
c.
B 10,7
C 5,0
Y
4,10
2,5
7,3
Z
8,5
8,6
9,1
2. (2 point) Find (a) ISD strategies and (b) symmetric Nash equilibria (pure and mixed)
of the following game:
X
Y
Z
A 0,0 1,2 2,1
B 2,1 0,0 1,2
C 1,2 2,1 0,0
3. (2 points) From the movie A Beautiful Mind : there are 4 men at the bar, and 5 women:
one blonde and 4 brunettes. Each man decides a woman (blonde or brunette) to hit on,
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simultaneously. Suppose the brunettes are equally attractive to the men, with appeal b.
The blonde is more attractive, with appeal a > b. If more than one man attempts to hit
on the blonde, they succeed neither with the blonde (they block each other), nor with any
brunette (the latter feel slighted). Any man choosing not to hit on the blonde succeeds with
a brunette, for a payoff of b. If a man is the only one who hits on the blonde, he succeeds,
with a payoff of a. Find all Nash equilibria of this game (both pure and mixed).
See https://www.youtube.com/watch?v=CemLiSI5ox8 for the scene from the movie.
4. (2 points) Player I holds a black Ace and a red 8. Player II holds a red 2 and a black
7. The players simultaneously choose a card to play. If the chosen cards are of the same
color, Player I wins. Player II wins if the cards are of different colors. The amount won
is a number of dollars equal to the number on the winner’s card (Ace counts as 1.) Thus,
if Player I plays black Ace while Player II plays red 2, Player I gets a payoff of −2 (loses
two dollars), and Player II gets a payoff of 2 (wins two dollars); and likewise for the other
strategy profiles.
Set up the payoff matrix, find the Nash equilibrium, and calculate each player’s expected
payoff in the equilibrium.
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