Economics 3M03, Spring 2016
Mid-term Exam 1 Answer Key
1. In each game below, nd all Nash equilibria (just circle the equilibria, you dont
need to prove that the circled action proles are Nash equilibria). If you believe that the
game does not have Nash e
Your name here_
Period _
_
Prompt Analyze the changing relationships between Native Americans along the Atlantic seaboard and the
English during the course of the seventeenth century.
Historical Context
Early colonization by British. Colonists who arrived
Economics 3M03, Spring 2016
Practice Problems 1: Answer key
1. Consider the following game between players 1 and 2.
2
M
5; 2
3; 4
6 ;5
L
U 3 ;3
1 I 2; 9
D 0; 5
R
4 ;3
4 ;5
1; 4
Find all Nash equilibria in the game by:
(a) cell-by-cell inspection;
(b) best
Document-Based Questions
A65
DBQ 2
English-Indian Relations, 16001700
Directions: In this DBQ, you must compose an essay that uses both your
interpretation of Documents AH and your own outside knowledge of the period
mentioned in this question.
Discuss t
1
APUSH
Mr. Laird
DBQ Summer Assignment
Instructions: Read the necessary background information in the text: Chapters 1-3 before
analyzing the documents, then tackle this. I have analyzed the first doc for you on the DBQ
Document Analysis Worksheet. Follo
Introduction to Game Theory
Part 6: Applications of Nash equilibrium (Bertrand Oligopoly)
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McMaster University
February 1, 2016
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February 1, 2016
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NE: Bertrand Oligopoly
2 rms, i
Introduction to Game Theory
Part 2: Examples of games
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McMaster University
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Introduction to Game Theory
January 11, 2016
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Prisoners dilemma
Consider a 2x2 game, i.e., a game between 2 playe
Introduction to Game Theory
Part 5: Dominance
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January 18, 2016
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Actions versus strategies
In normal-form games, the set of actions coincide
Introduction to Game Theory
Part 1: Introduction
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What is game theory?
Game theory formalizes strategic interaction betwee
Introduction to Game Theory
Part 4: Best Response
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Finding Nash equilibria: cell-by-cell inspection
There are several meth
Part I: Representing Games
(Chapter 1-5)
1
Introduction
(Chapter 1-3)
Game Theory: Definitions and overview
Representation: Extensive forms
Strategies
Representation: Normal forms
2
Its Your Move
3
What is a game?
A game is being played whenever peop
Nash Equilibrium
(Watson Chapters 9, 10, 11)
1
Pure Strategy Nash Equilibrium
A set of strategies forms a Nash equilibrium if the
strategies are best replies to each other
Recall: A strategy is a best reply to a particular strategy of another player
if i
Part III:
Analysis of Dynamic Settings
1
Outline
Backward induction, subgame perfection (Ch.14-16)
Bargaining* (Ch.18-19)
Repeated games, and applications (Ch. 22-23)
2
Details of the ExtensiveForm
Chapter 14
3
Game Trees: Basic Language
Recall: Trees
Strictly Competitive Games
and Security Strategies
(Chapter 12)
1
Strictly Competitive Game
In a strictly competitive game, the two players have exactly opposite
rankings over the outcomes. Wherever one players payoff
increases, the other ones payoff dec
Repeated Games and
Applications
Chapter 22, 23
Dynamic game
People often interact in ongoing relationships
Employment relationships
Countries competing over tariff levels
Players condition their decisions on the history
of their relationship
An employee
Part IV:
Information
1
Outline
Random Events and Incomplete Information (Ch.24)
Bayesian Nash Equilibrium, and applications
(Ch.26-27)
Perfect Bayesian Nash Equilibrium, and applications
(Ch. 28-29)
2
Random Events and
Incomplete Information
Chapter 24
ECON 3M03 Spring 2013 Quiz 3
Version 1
In a variation of the Bertrand model, there are two firms each with costs
TCi = 3qi i = 1, 2 . They sell in a market where demand for their output is QD = 20 P .
Each firm simultaneously chooses a price which can be
Introduction to Game Theory
Part 3: Nash Equilibrium
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McMaster University
January 11, 2016
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Introduction to Game Theory
January 11, 2016
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Simultaneous-move games of complete information
Simultaneous-move ga
Introduction to Game Theory
Part 10: Extensive games of perfect information
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McMaster University
April 19, 2016
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April 19, 2016
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Extensive Form Games of perfect information
In
Introduction to Game Theory
Part 8: Strategic-form Games with Mixed Strategies
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McMaster University
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Mixed Strategies
Many games do not ha
Economics 3M03, Spring 2016
Solutions to Practice Problems 2
1. Each of two rms has one job opening. The rms oer dierent wages: rm 1 oers the
wage $10 per hour, and rm 2 oers the wage $12 per hour. There are two workers, each of
whom can apply to only one
Economics 3M03, Spring 2016
Practice Problems 1
1. Consider the following game between players 1 and 2.
2
L M R
U 3; 3 5; 2 4; 3
1 I 2; 9 3; 4 4; 5
D 0; 5 6; 5 1; 4
Find all Nash equilibria in the game by:
(a) cell-by-cell inspection;
(b) best response fu
Economics 3M03, Spring 2016
Mid-term Exam 2 Answer Key
1. Consider a game between two players with the following payos of player 1. Suppose
that player 2 randomizes between L and R with probabilities q and 1 q, respectively.
(a) Determines the pure strate
Economics 3M03, Spring 2016
Problem-Solving Session 1: Answer key
1. Exercise 17.1 from the textbook.
X Y
X 3; 3 1; 5
Y 5; 1 0; 0
The game above is NOT the Prisoners Dilemma as Player 1 prefers (X; X) to (Y; Y ).
Also, Y does not strictly dominate X for e
Economics 3M03, Spring 2016
Practice problems for the nal exam
Note 1: the nal exam is comprehensive.
Note 2: I will keep my regular o ce hours on Monday at 11am-12pm and 1pm-2pm. Please see me to discuss
solutions.
Extensive-form games of perfect informa
Department of Economics
McMaster University
Class: Econ 3M03
Winter 2016
Introduction to Game Theory
Class location/time: DSB B105/Monday 2:30PM3:20PM, Wednesday 2:30PM4:20PM
Instructor: Maxim Ivanov
Office: 408 KTH
Office hours: Monday, 1:00PM2:00PM
Emai
Econ 3M03
Problem-solving Session 1 (Chapters 1-3)
1. Solve Exercise 17.1 from the textbook.
2. Show that the Rock-paper-scissors game does not have a Nash equilibrium in pure
strategies. Put the payoff of each player 1 in the case of winning, -1 in the c
Introduction to Game Theory
Part 9: Mixed-Strategy Nash Equilibria
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McMaster University
February 29, 2016
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Introduction to Game Theory
February 29, 2016
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Set of mixed strategies
Let i be the set of all m
Economics 3M03, Spring 2016
Practice Problems 2
1. Each of two rms has one job opening. The rms oer dierent wages: rm 1 oers the
wage $10 per hour, and rm 2 oers the wage $12 per hour. There are two workers, each of
whom can apply to only one rm. The work
Introduction to Game Theory
Part 6: Applications of Nash equilibrium (Cournot Oligopoly)
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McMaster University
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Application of NE: Cournot Oligo