Econ GU4415: Problem Set #1
Qingmin Liu
Columbia University
September 19, 2016
Abstract
Due in class on September 26, 2016. See the syllabus for problem set
policies.
1. Consider the following two-player game:
A
B
C
D
L
4; 2
1; 4
0; 0
0; 0
M
0; 0
1; 4
2;
Game Theory Midterm 1 Solutions
October 3, 2016
1. Three game theorists work on a team project. Assume they work independently, and it is not possible
for them to monitor each other. No one likes working, and the cost of effort is measured in dollars.
Eac
Econ GU4415, Spring 2017
Problem Set #1 Solutions
1. What is the definition of a strictly dominated strategy? What is the definition of a
weakly dominated strategy? Give an example of a two-player game (in matrix form)
in which one player has three pure s
Econ W4415: Problem Set #1
Qingmin Liu
Columbia University
Jan. 26, 2016
Abstract
Due in class on Feb. 4, 2016. See the syllabus for problem set policies.
1. Consider the following two-player game:
L
A 4; 2
B 1; 4
C 0; 0
D 0; 0
M
0; 0
1; 4
2; 4
0; 0
N
5;
Game Theory
Problem Set 9
Levent Kokesen
1. Consider the following prisoners dilemma game.
C
D
C
2; 2
3; 0
D
0; 3
1; 1
For what values of ; if any, the following strategies constitute subgame perfect equilibria?
(a) Tit-For-Tat: Choose C in period 1 and t
Econ 171 Spring 2010
Problem Set 3 - Solutions
Due Tuesday, June 1
Important: hand in only the two-star problems. There are no one-star problems on this
problem set. The notation a.b denotes problem number b from Chapter a in Watson.
* Problem 1
Consider
Economics 379
Game Theory
Department of Economics
Colby College
Problem Set 1
Due in class Wednesday, February 23
From Dutta
CH 3: Exercises 1, 2, 8 - 10, 11 - 14
CH 5: Exercises 5.7 - 5.13
Additional Exercises
1. Determine the set of strategies that surv
Game Theory
Problem Set 5
Levent Kokesen
1. Find all the pure and mixed strategy equilibria of the following games by constructing
the best response correspondences of the players:
(a) Matching Pennies:
H
T
1; 1 1; 1
1; 1 1; 1
H
T
(b) Hawk-Dove:
H
D
H
D
0
Columbia University Department of Economics
W4415 Game Theory
Midterm Solutions
Prajit Dutta
October 15th
Problem 1: Definitions (10 Points)
Provide formal definitions of the following concepts:
(a) Strategy si weakly dominates strategy s0i . [5p]
Strateg
Columbia University Department of Economics
W4415 Game Theory
Problem Set 4
Prajit Dutta
Due Wednesday, October 7th, 2014 in class
1
Mixed Strategies
Consider the game represented in the following payo matrix.
1\2
H
D
H
0, 0
2, 8
D
8,2
4, 4
(a) List all p
Economics 379
Game Theory
Department of Economics
Colby College
Problem Set 5
Due Wednesday, April 14, 2011
From Dutta
Chapter 15: Exercises 11, 12, 15, 17, 20 23 (Note: For question 22, use a discount rate of 0.9)
Additional Exercises
1. Find conditions
Game Theory
Problem Set 6
Levent Kokesen
1. Two people are involved in a dispute. Person 1 does not know whether person 2 is strong
or weak; she assigns probability to person 2 being strong. Person 2 is fully informed.
Each person can either ght or yield.
Economics 379
Game Theory
Department of Economics
Colby College
Problem Set 2
Solutions
Chapter 6
6.8
Firm 1s profit maximization problem is:
max( a bq1 dq2 ) q1 cq1
q1
FOC : a 2bq1 dq2 = c q1 =
a c dq2
2b
ac
a c dq2
is nonnegative so long as q2
. Thus f
Game Theory
Problem Set 5 Solutions
Levent Kokesen
1. Find all the pure and mixed strategy equilibria of the following games by constructing
the best response correspondences of the players:
(a) Matching Pennies:
H
T
1; 1 1; 1
1; 1 1; 1
H
T
Let 1 (H ) = p
Columbia University Department of Economics
W4415 Game Theory
Midterm Solutions
Prajit Dutta
October 16th, 2013, in class.
Notes:
This exam is worth 100 points, and will last 75 minutes. Answer all the questions. You
are advised to divide your time among
Columbia University Department of Economics
S4415Q Game Theory, Problem Set 3
Due Monday August 1st in class.
Problem 1
Suppose two players play an infinitely repeated version of the stage game represented in the
following payoff matrix:
1\2
A
B
A
2, 2
0,
Columbia University Department of Economics
W4415 Game Theory
Problem Set 2
Prajit Dutta
Due September 23th, 2015 in class
1
Dominant and Dominated Strategies
Consider the game represented in the following payo matrix.
T
M
B
L
8, 12
6, 14
16, 10
C
14, 2
2
Game Theory (S4415): Answers to Problem Set 4
Prajit K. Dutta
June 22, 2001
Chapter 13
1.4 Write down the extensive form of the game above. How many subgames are there in this game? How many strategies does Coke have?
Answer:
Coke
Pepsi
-2,-1
A
T
-3,1
A
E
Game Theory
Problem Set 1
Levent Kokesen
1. Consider the following game of divide the dollar. There is a dollar to be split between
two players. Player 1 makes an oer (an oer by Player 1 species how much he would
like Player 2 to have). Without observing
Perfect Bayesian Equilibrium
Game Theory, Summer 2016
1
Sequential Games
In 4.1 we looked a simultaneous game with incomplete
information. The players played simultaneously, but one (or
more) had private information that made the other uncertain
which pay
Game Theory - W4415
Solutions to Final Examination
Levent Kokesen
December 20, 1999
1. (25 pts) Consider the following extensive form game. Player 1 either goes hunting with
player 2 in which case they engage in the following Stag Hunt game
S
H
S
3; 3
1;
Assorted Extras
Game Theory, Summer 2016
1
Strategies
Throughout the week weve used relatively simple strategies:
History-independent strategies.
This includes strategies which are time independent - i.e.
always play C in all periods and for all histori
GU4415: Game Theory
Lecture 5
Rationalizability,
Pure Strategy Nash Equilibrium
Last Time
1. Weak Dominance: Application, Pitfalls of Iteration
2. Mixed Strategies and (Iterated) Strict Dominance
3. (Never) Best Responses
4. Rationalizability
Rationalizab
2/7/17
GU4415: Game Theory
Lecture 7
Market Games,
Mixed Strategy Nash Equilibrium
Last Time
1. Pure Strategy Nash Equilibrium & Examples
2. Introduced Cournot Oligopoly
1
2/7/17
Cournot Oligopoly
N1 firms in a market (Monopoly if N=1; Duopoly if N=2)
S
2/2/17
GU4415: Game Theory
Lecture 6
Pure Strategy Nash Equilibrium,
Market Games
Last Time
1. Rationalizability & Application
2. Pure Strategy Nash Equilibrium
1
2/2/17
Nash Equilibrium: Definition
Definition: (s1,sN) is a Pure Strategy Nash Equilibrium
1/27/17
GU4415: Game Theory
Lecture 4
Weak Dominance, Mixed Strategies, Best
Responses, Rationalizabiliy
Last Time
1. IDSDS & Applications
2. Weak Dominance
1
1/27/17
Weak Dominance Reminder
A strategy weakly dominates another if the former does at least
1/17/17
GU4415: Game Theory
Lecture 1
Today: Introduction and Logistics
What is Game Theory?
A methodology/toolkit for studying strategic situations
What is a strategic situation?
Begin with what it is not
Consumers take prices as given when deciding con
1/24/17
GU4415: Game Theory
Lecture 3
Iterated Deletion of Strictly Dominated
Strategies, Weak Dominance
Last Time
1. Normal form games, common knowledge of the game (=
complete information), common knowledge of rationality
2. A rational player should not
1/19/17
GU4415: Game Theory
Lecture 2
Normal Form Games, Dominance,
Iterated Dominance
Game Theory
Recall from last time:
Game Theory is multi-person decision theory
To understand how a (rational) player should act,
we need to understand what the struct