CAS EC 403 Game Theory
Assignment 1
Solution
1. (W3.2) Suppose a manager and a worker interact as follows. The manager decides
whether to hire or not hire the worker. If the manager does not hire the worker, then
the game ends. When hired, the worker choo

CAS EC 403 Game Theory
Midterm Exam
3/21/14
I Please write your answers in the blue books provided
I Write your name on the blue book in pen
I Good luck!
1. Let G = (N; S; u) be a normal-form game. Restricting attention to pure strategies,
give a formal d

CAS EC 403 Game Theory
Assignment 1
Due 9/21/15
1. (W3.2) Suppose a manager and a worker interact as follows. The manager decides
whether to hire or not hire the worker. If the manager does not hire the worker, then
the game ends. When hired, the worker c

CAS EC 403 Game Theory
Assignment 2
Due 10/5/15
1. Find the pure strategy Nash equilibria in the following games:
1=2
A
B
D
E
F
2; 3
3; 0
10; 4
4; 5
G
8; 2
4; 5
6; 1
2; 3
H
7; 4
6; 4
3; 9
5; 2
1=2
A
B
D
E
F
1; 1
1; 2
3; 2
2; 0
G
3; 1
1; 2
2; 1
3; 0
H
0; 2

EC 403 Game Theory, Boston University
Summer 2, 2013
Problem Set 5 - Answer Key
Question 1.
Consider a principal-agent game identical to the one described in class, except for the probability
of a good outcome following the choice of high effort, which is

EC 403 Game Theory, Boston University
Summer 2, 2013
Problem Set 5
Question 11
Repeat the analysis of the principal-agent model presented in class, but consider a more general
case: p, that is, the probability of success following high effort, can take an

EC 403 Game Theory, Boston University
Summer 2, 2013
Final exam - Answer Key
Question 1
1.a) The profits of firm A are:
(3 pA )pA if pA < pB ,
(3pA )pA
2
if pA = pB ,
0 if pA > pB .
Profits for firm B can be computed in the same way. The matrix of payoffs

EC 403 Game Theory, Boston University
Summer 2, 2013
Problem Set 1 - Answer Key
Question 1
a) A ranking of teams based on winning percentages is complete and transitive.
To show that, consider any pair of teams a and b with, respectively, percentage of wi

EC 403 Game Theory, Boston University
Summer 2, 2013
Midterm 1
Total: 100 points. Time: 90 minutes.
Question 1. (40 points)
1.a) (10 points) Explain (briefly) why games can have at most one equilibrium in weakly dominant
strategies.
For each of the follow

EC 403 Game Theory, Boston University
Summer 2, 2013
Problem Set 4 - Answer Key
Question 1
Stage game a has 2 pure-strategy Nash Equilibria: (U, R) and (D, L). You should therefore check
whether vectors of actions which are not NE of the stage game can be

EC 403 Game Theory, Boston University
Summer 2, 2013
Problem Set 3
Question 1
Solve these games using backward induction.
a)
1
b)
1
G
3,8
C
7,9
H
2
A
D
I
1
1,2
J
1
1
B
E
2,1
10,4
K
0,5
L
2
F
1
M
4,0
N
6,5
c)
2
3
Question 2.
Consider the following game.
Th

EC 403 Game Theory, Boston University
Summer 2, 2013
Midterm 2 - Answer Key
Question 1
1.a) Game I has 3 subgames, game II has 2 subgames.
1.b) The unique SPNE in game I is (A, F ), (D). The game is a game of perfect information,
therefore the SPNE corres

EC 403 Game Theory, Boston University
Summer 2, 2013
Problem Set 4
Question 1
Consider the following stage games:
a)
1/2
L
C
R
U
0, 0
0, 0
1, 1
M
0, 0
2, 2 0, 2.5
D
0, 0, 0, 0
0, 0
b)
L
C
R
U
0, 0
0, 0
1, 1
M
1, 0
2, 2 0, 2.5
D
0, 0, 0, 0
1/2
0, 0
Define

EC 403 Game Theory, Boston University
Summer 2, 2013
Problem Set 2 - Answer Key
Question 1
The game has the following Nash Equilibria:
(N orth, (East, W est), (N orth, (East, South), (N orth, (W est, South),
(East, (N orth, W est), (East, (N orth, South),

EC 403 Game Theory, Boston University
Summer 2, 2013
Midterm 2
Total: 100 points. Time: 90 minutes.
Question 1 (35 points)
1.a) (10 points) How many subgames are there in game I? And in game II?
1.b) (25 points) Find all the Pure-Strategy Subgame Perfect

EC 403 Game Theory, Boston University
Summer 2, 2013
Problem Set 3 - Answer Key
Question 1
a) The backward induction solution is (B, G, J, L, N ), (C, E).
b) The backward induction solution is (A, H, J, K, N ), (C, F ).
c) The backward induction solution

EC 403 Game Theory, Boston University
Summer term 2, 2013
Final
Total: 100 points
Question 1. (25 points)
Consider the following model of price competition. Two firms, A and B, set prices (pA and pB ) in
a market whose demand curve is given by the equatio

EC 403 Game Theory, Boston University
Summer 2, 2013
Problem Set 2
Question 1.
Find the pure strategy Nash Equilibria of the following game (Colonel Blotto game, pag 37).
Tlobbo/Blotto North,East North,West North,South East,West East,South West,South
Nort

Exercises
1) Let the game be defined as the infinite repetition of the following stage-game:
1/2 c
n
c
1, 1 3, 0
0, 5 2, 2
n
where both players have the same discount factor (0, 1). Consider the following strategy
(tit-fot-tat):
- choose n in round 1,
- f

EC 403 Game Theory, Boston University
Summer 2, 2013
Midterm 1 - Answer Key
Question 1.
1.a) Each player has at most one weakly dominant strategy. Therefore a game can have at most
one equilibrium in weakly dominant strategies.
I)
1/2
L
R
U
1, 3
2, 2
M
2,

CAS EC 403 Game Theory
Assignment 3
1. Consider a two player game in which player 1 can choose A or B. The game ends if he
chooses A while it continues to player 2 if he chooses B. Player 2 can then choose C
or D, with he game ending after C and continuin

CAS EC 403 Game Theory
Assignment 4
Solution
1. 18.2
Solution: John should undertake the activity that has the most impact on t, and hence
his overall payo, per time/cost. A one-unit increase in x will raise t by J . A oneunit increase in w raises t by 1

CAS EC 403 Game Theory
Assignment 5
Due 11/30/15
1. Consider the following stage game:
1=2
U
M
D
L
3; 1
1; 3
0; 0
M
9:5; 0
5; 5
3; 1
R
0; 0
0; 9
1; 3
(a) Find the NE in the stage game.
(b) Suppose the repeated game G(T; ) = G(2; 1): Can the outcome (5; 5)

CAS EC 403 Game Theory
Assignment 5
Solution
1. Consider the following stage game:
1=2
U
M
D
L
3; 1
1; 3
0; 0
M
9:5; 0
5; 5
3; 1
R
0; 0
0; 9
1; 3
(a) Find the NE in the stage game.
(b) Suppose the repeated game G(T; ) = G(2; 1): Can the outcome (5; 5) be

CAS EC 403 Game Theory
Assignment 6
Due 12/7/15
1. Two investors i = 1; 2 simultaneously decide how much to invest in a joint project. If
investor i has type i and invests xi
0, while her partner invests and xj
0; her
payo is:
ui (xi ; xj ; i ) = i xi xj

CAS EC 403 Game Theory
Assignment 6
Solution
1. Two investors i = 1; 2 simultaneously decide how much to invest in a joint project. If
investor i has type i and invests xi
0, while her partner invests and xj
0; her
payo is:
ui (xi ; xj ; i ) = i xi xj x3

CAS EC 403 Game Theory
Final Exam
12/15/14
Solution
I Answer any four of the ve questions
I Please write your answers in the blue books provided
I Please hand in exam sheet with your blue book
I Good luck!
1. Recall the two-by-two coordination game:
1=2 S

CAS EC 403 Game Theory
Final Exam
12/15/14
Solution
I Answer any four of the ve questions
I Please write your answers in the blue books provided
I Please hand in exam sheet with your blue book
I Good luck!
1. Recall the two-by-two coordination game:
1=2 S

CAS EC 403 Game Theory
L1: Games on Normal Form
Bjorn Persson
Boston University
9/2/15
Bjorn Persson (Boston University)
I Representing games
9/2/15
1 / 14
Strategic Interaction I
What is game theory?
A mathematical formulation of strategic interaction
A

EC 403 Game Theory, Boston University
Summer 2, 2013
Problem Set 1
Question 1. (Ex 27.7,27.8 pag 445).
a) Suppose sport teams in a league like NBA are ranked by their winning percentage (i.e. the
fraction of games that each team has played that it actuall