University of Calgary
Department of Economics
Econ373
Midterm: Answer Key
Question 1:
As the textbook.
Question 2:
(a) Let M denote the number of people other than a representative person who donate 0
day of labor to assemble the ride. For each person, th

Part B
Nash equilibria will consist of a strategy for each player where he is best responding by taking into
account his preferences and the actions of the other four players. In this case the Nash equilibria are:
All 5 voters vote for A
4 voters vote for

University of Calgary
Department of Economics
Econ373
L. Yuan
Assignment 2: Due date is at 11:00 am in class on February 10, 2016. You are
encouraged to work in pairs. The two students working together may hand in one
assignment and get the same mark. Ple

University of Calgary
Department of Economics
Econ373
Assignment 2: Answer Key
Question 1:
Part A:
Because the two firms collude in their production decision, we can consider the sum of
their production as q, that is, = + , then we can get
= = (100 0.002

Econ 373: Midterm II Solutions
L. Yuan
Winter 2016
Prof.
1. Two pure strategy Nash equilibria (R, R) and (L, L).
L (q)
R (1-q)
L (p)
12, 12
2, 2
R (1-p)
2,2
8,8
Find mixed strategy:
Let p=probability of playing L for player 2 (then Prob(R) = (1-p)
Let q=p

reg @Jél'QQm-ﬁf (EV?
f
76% 3
Quiz 1
Econ 373, Fall 2015
Student’s Name:
Answer both questions in the space provided.
The Game: This game involves two players, a brother, BRO, and sister,
SIS. BRO and SIS are fanatical hockey fans. Their dad has two ti

University of Calgary
Department of Economics
Econ373
Assignment 3: Answer Key
:
.
Problem 1:
Let pL and pR be the probabilities which Row player choose L or R, qL and qR be the
probabilities which Column choose L or R
Choices
Row player's expected payoff

University of Calgary
Department of Economics
Econ 373
L.Yuan
Assignment 1: Due Date is January 29, 2016 at 11 AM (in class). You are encouraged to work
in pairs. Two students working together may hand in one assignment and get the same mark.
Please inclu

2
The Extensive Form
2.
M
0, 0, 0
n
W
h
D
0, 1, 1
w
s
O
1, 1, 1
w
S
O
h
s
n
1, 0, 0
1, 1, 1
0, 0, 0
4.
R
P
S
2
R
1
P
S
0, 0
1, 1
1, 1
R
P
S
1, 1
R
P
S
1, 1
0, 0
1, 1
1, 1
0, 0
The order does not matter as it is a simultaneous-move game.
73
Instructor's

27
Lemons, Auctions,
and Information Aggregation
2.
Your optimal bidding strategy is b = v/3. You should bid b(3/5) = 1/5.
4.
(a) Colin wins and pays 82.
(b) Colin wins and pays 82 (or 82 plus a very small number).
(c) The seller should set the reserve pr

18 BARGAINING PROBLEMS
120
Note: The efficient allocation (who gets to produce) is reached in both (a)
and (b), but the payoffs differ based on who has the property right. The
physician and the confectioner care about which of them has the property
right.

6
Dominance and best response
2.
(a) To determine the BR set, we must determine which strategy of player 1
yields the highest payoff given her belief about player 2s strategy selection. Thus, we compare the payoff to each of her possible strategies.
u1 (U

10 OLIGOPOLY, TARIFFS, CRIME, AND VOTING
94
The first-order condition is 8 R1 4 0. Rearranging yields R1 = 4,
which implies R2 = 16, and the total number of fish caught is 24+64 =88.
(c) With the tax, the payoff from fishing at Reef 1 is 8 R1 /2 x, which

28
Perfect Bayesian Equilibrium
2.
(a) No.
(b) Yes. (AA0 , Y) with belief q 35 .
(c)
2
1
X
Y
AA
4,3
4,3
AB
5,2
2,5
BA
5,3
2,1
BB
6,2
0,3
4.
Yes. Player 1s actions may signal something of interest to the other
players. This sort of signaling can arise in e

8
Location, Partnership, and Social Unrest
2.
For x < 80, locating in region 2 dominates locating in region 1.
4.
Recall from the text that BR1 (y) = 1 + cy, and BR2 (x) = 1 + cx. Assume
1 < c < 0. This yields the following graph of best-response function

3
Strategies and the Normal Form
2.
No, not hire does not describe a strategy for the manager. A strategy for the manager must specify an action to be taken in every contingency. However, not hire does not specify any action contingent upon
the worker bei

12
Strictly Competitive Games
and Security Strategies
2.
(a) 1: C; 2: Z
(b) 1: C; 2: Z
(c) 1: A; 2: X
(d) 1: D; 2: Y
4.
Let i be one of the players, and let j be the other player. Because s
is a Nash equilibrium, we have ui (s) ui (ti , sj ). Because t is

10
Oligopoly, Tariffs, Crime, and Voting
2.
1
(a
m
pi )[pi c]
if pi = p
where m
0
if pi > p,
denotes the number of players k cfw_1, 2, . . . , n such that pk = p.
(a) Si = [0, ], ui (pi , pi ) =
(b) The Nash equilibrium is: pi = c for all i. For n > 2, t

Econ 373
L.Yuan
April 2, 2009
Reading Assignment: Chapter 8
The Repeated PD as A Metaphor for Life
The PD is the most famous of all games, because it captures the essence of
a huge class of important games. Recall that it was one of the rst games we
looke

ECON 373 Game Theory & Strategic Thinking for Social Sciences
Handout on Mixed Strategies
Instructor:
Ben
Polak, Akio
Econ Yamazaki
159a/MGT522a
October 4, 2007
Strategies
The main lesson of the last class was theMixed
following:
Main Lesson If a mixed st

ECON 373 Game Theory & Strategic Thinking for Social Sciences
Instructor: Akio Yamazaki
Partnership Game
In this weeks classes, we talked about Partnership game. And in the beginning of todays
lecture, my hope was to discuss about the negative externality

ECON 373 Game Theory & Strategic Thinking for Social Sciences
Instructor: Akio Yamazaki
Why Derivatives and How
In this supplementary note, I will briefly explain why we need to deal with derivatives to analyze
a game and show you a technique to take deri

ECON 373 Game Theory & Strategic Thinking for Social Sciences
Instructor: Akio Yamazaki
Some definitions
Pareto efficient an outcome is Pareto efficient if it is not possible to improve the pay-off of one
player without lowering the pay-off of another
Par

ECON 373 Game Theory & Strategic Thinking for Social Sciences
Instructor: Akio Yamazaki
Mathematical Notations for Class 1
Math notation
English
in (an element of)
for all
actions of players other than
player
AB
A = cfw_,
I strictly prefer A over B
set

21 INVESTMENT AND HOLD UP
130
10.
(a) S = x + 2y. According to the standard bargaining solution,
uP = P S+uP = g(x+2y)x2 +w, uA = A S+uA = (1g)(x+2y)y 2 w.
Since uA = y 2 + t w in the game, t = (1 g)(x + 2y).
(b) The principal chooses x to solve maxx (g(x

14
Details of the Extensive Form
2.
Suppose not. Then it must be that some pure-strategy profile induces
at least two paths through the tree. Since a strategy profile specifies an
action to be taken in every contingency (at every node), having two paths
i

29
Job-Market Signaling and Reputation
2.
Consider separating equilibria. It is easy to see that NE0 cannot be an
equilibrium, by the same logic conveyed in the text. Consider the workers
strategy of EN0 . Consistent beliefs are p = 0 and q = 1, so the fi

Econ 373
L. Yuan
Lecture Notes 5
Objectives for Today
to talk about the essentials of equilibrium thinking
to introduce one new, really important concept, best response
to introduce some renements of concepts already encountered, nonstrict (or
weak) Nash

Econ 373
L. Yuan
March 19, 2009
Reading Assignment: Chapter 4 in your text book.
We will rst talk about the Hawk/Dove game and then start the
sequential games.
The Hawk/Dove Game: The Hawk/Dove game is an evolutionary game among a bunch of birds of the sa