Repeated Games Practice Problems
1) Ike and Monty play the following game:
Monty
West
East
North
5,4
2,3
South
4,1
3,7
Ike
They play the game twice. There is no discounting.
a) Identify all pure-strategy Nash equilibria in the stage game.
(N,W) , (S,E)
b)
Sample Problem on Subgame Perfection
1)
Suppose a US firm and an EU firm are duopolists in the
market for a good which is consumed only in Brazil.
Brazilian demand is given by the inverse demand
function
p = max(0, a-b(x +x*),
where x is US output and x*
ECON 451
PROBLEM SET #3; Due Monday, 2/24/14
1) For each of the following games, find the complete set of Nash Equilibria (in pure and
mixed strategies).
a)
I
/
II
5,4
1,1
1,1
4,5
-4,-3
3,-2
-2,2
1,0
b)
I
/
II
c)
I
/
II
L
C
R
T
10,5
8,3
5,10
M
5,8
10,6
9,
ECON 451
PRACTICE PROBLEM SET #2
1.
Find the complete set of Nash equilibria (in pure and mixed strategies) in the
following games:
A.
II
a1
I
a2
5,4
b2
1,1
b1
1,1
4,5
a1
a2
-4,-3
b2
3,-2
b1
-2,2
1,0
B.
II
I
C.
II
U
I
2.
L
1,1
R
3,0
D
3,0
2,2
(A simple mo
Playing Forever: Repeated Interaction
with Infinitely Lived Players
13
1. There are three fishermen, and each day they individually decide how many boats to send
out to catch fish in the local lake. A fisherman can send out one or two boats, and the daily
Keep Em Guessing: Randomized Strategies
7
1. Reproduced in FIGURE PR7.1 is the telephone game from Section 4.2. Find all Nash equilibria in mixed strategies.
FIGURE PR7.1 The Telephone
Game
Winnie
Call
Call
0,0
2,3
Wait
Colleen
Wait
3,2
1,1
ANSWER: Let p
Name:_
PUID:_
Signature:_
Econ 451: Spring 2014
Midterm 1
2/26/14
Form A
Answer the 5 following questions. The points value for each is given at the top of
the respective page. Your total score will be out of 100 points. Feel free to show
work on the back
Dynamic Games of Perfect Information Practice Problems
1) There are two players, Hillary and Jackie. Hillary has two actions available: cfw_A, B. Jackie has
A
B
two actions, as well: cfw_C, D. Hillary chooses her action first. After observing Hillarys cho
Stackelberg Duopoly Practice Problems
1) Consider a market with inverse demand given by:
There are two firms within this market, firm 1 and firm 2. Firm 1 first sets its quantity
and then after observing firm 1s choice, firm 2 will set its quantity.
Let a
Advanced Mixed Strategy Practice Problems:
Player
1
T
M
B
Player 2
L
R
3,2
7,4
4,1
6,0
2,8
8,5
1) Find all Nash equilibrium where the probability each player places on all strategies is
positive (neither player plays any strategy with 0 probability):
3 wa
Name:_
PUID:_
Signature:_
Econ 451: Game Theory
Final - Form A
6/7/2013
Answer the following 5 questions. Make sure to show all work. Partial credit will be
given. The point value for each question is listed at the top of each page. Extra Paper is
include
Dynamic Games of Perfect Information Practice Problems
1) There are two players, Hillary and Jackie. Hillary has two actions available: cfw_A, B. Jackie has
A
B
two actions, as well: cfw_C, D. Hillary chooses her action first. After observing Hillarys cho
Econ 451 Practice Problems Dominant Strategies and Nash Equilibrium
a) Write your procedure of IEDS:
b) What is the IEDS equilibrium?
d) List all Nash Equilibria:
2)
a) Label each strategy for each player as: weakly dominated, strictly dominated, and
undo
Practice Problems: Mixed Strategies
1)
Player
1
A
Player
2
T
B
Player
3
L
3,5,4
5,3,2
B
Player 3
R
8,2,3
6,3,2
Player
2
T
B
L
4,8,1
3,7,2
R
6,1,4
7,2,1
If Player 1 plays (A, player 2 plays , and player 3 plays L, what are each players expected
payoffs?
2)
Imperfect Information Practice Problems:
For each question
a) Show the extensive form of the game (game tree)
b) List all pure-strategy Nash Equilibria
c) List all pure-strategy SPNE
1) Complete information game where Player 1 moves firsts:
L1 ,
L2
1,2
7,
Imperfect Information Practice Problems:
For each question
a) Show the extensive form of the game (game tree)
b) List all pure-strategy Nash Equilibria
c) List all pure-strategy SPNE
1) Complete information game where Player 1 moves firsts:
L1 ,
L2
1,2
7,
Stackelberg Duopoly Practice Problems
1) Consider a market with inverse demand given by:
There are two firms within this market, firm 1 and firm 2. Firm 1 first sets its quantity
and then after observing firm 1s choice, firm 2 will set its quantity.
Let a
Dynamic Games Practice Problems (2)
1)
a) Find all pure-strategy SPNE
b) Find all SPNE (pure and mixed)
c) Can you find one Nash Equilibrium that is not a SPNE?
One example of many:
Dynamic Games Practice Problems (2)
2)
a) Find all pure-strategy SPNE
b)
Game Theory ECON 45100-003 Spring 2017
Problem Set 1
Due : Tue, Jan 24. Hand in your problem set solutions in class.
1
Question 1.
Going to the Movies: There are two movie theatres in your neighborhood: Cineclass, which is located
one mile from your home,
ECON 451 - Game Theory
Purdue University - Spring 2017
1
Course Description
Economics 451 is a course in game theory, a mathematical theory of interactions among decisionmakers. The goal of this class is to introduce the students to the basics of game the