SOLUTIONS FOR EXERCISES IN: NORMAL FORM GAMES
ECON2112
Exercise 1.
(1) Strategies T and R are strictly dominated. The strategy prole (B, L) is an
equililibrium in dominant strategies and, therefore, it is a strict equilibrium
and a Nash equilibrium.
(2) S
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SCHOOL OF ECONOMICS
ECONOMICS 2112
GAME THEORY AND BUSINESS STRATEGY
S1 2011
MIDTERM EXAM
This exam comprises of 12 pages including this cover page.
There are 10 questions. Answer all 10.
Questions answered
Final-Practice Exam #2
Economics 101 Professor H. Quirmbach Final Exam
PRINT NAME_ STUDENT ID NO._ GROUP TIME_
SCORE_ INSTRUCTIONS: 1. Fill in all requested information above and on the answer sheet.
2. There are 40 multiple choice questions and one probl
ECON 2112. PROBLEM SET 2
DUE: AT THE BEGINNING OF YOUR TUTE IN WEEK 3.
Exercise 1. Consider a 3 person game. Let the pure best responses be as follows:
R1 (L, W) = cfw_T
R2 (T, W) = cfw_L, R
R3 (T, L) = cfw_E
R1 (L, E) = cfw_B
R2 (T, E) = cfw_L
R3 (T, R)
Normal form games and Nash equilibrium
ECON2112
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Normal form games and Nash equilibrium
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Course Structure
Lectures
Lecture notes will be available in the course website.
Most of the material is covered in: Game Theory for applied economists
by
Mixed strategies and Admissibility
ECON2112
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Mixed strategies and Admissibility
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Matching Pennies
Example
A game is played between two players, player 1 and player 2. Each
player has a penny and must secretly turn the penny to heads or
tails
ECON 2112. PRACTICE EXERCISES FOR WEEK 4
Exercise 1. Two players, 1 and 2, take turns choosing numbers; 1 goes first. On his turn, a player may
choose any number between 1 and 10, inclusive, and this number is added to a running total. When the
running to
ECON 2112. PROBLEM SET 3
DUE: AT THE BEGINNING OF YOUR TUTE IN WEEK 4.
Exercise 1. Write down the normal form game of the Rock, Paper, Scissors game. What is the Nash
equilibrium.? (You do not need to compute it explicitly, your intuition should tell you
ECON 2112. PRACTICE EXERCISES FOR WEEK 4: SOLUTIONS
Exercise 1. The player who brings the total to 100 wins, therefore if a players has to move and the current total is an
integer in the interval (90, 99) he can win by choosing a number equal to 100 minus
Normal form games: Applications
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Normal form games: Applications
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Normal form games
Definition (Finite Normal Form Game)
An n-player finite normal form game G = (S1 , S2 , . . . , Sn ; u1 , u2 , . . . , un )
consists of
for each pla
Extensive form games: perfect information
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Extensive form games: perfect information
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Introduction
In a normal form game, players take decisions simultaneously.
In an extensive form game, players take decisions sequentially.
A game
Game Theory and Business Strategy
Tutorial 10
Gary Liang
Semester 1, 2017
UNSW Australia
Perfect Bayesian equilibrium
A strategy profile AND a system of beliefs that satisfy:
R1: At any information set, the player with the move must have a belief about wh
ECON 2112. PROBLEM SET 1
DUE: AT THE BEGINNING OF YOUR TUTE IN WEEK 2.
Note: In some exercises below you will find the expression pure strategy. By that we mean the kind of
strategies that we have seen in class. In the second week we will introduce concep
Lecture 2
Admissibility and Mixed strategies
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Admissibility and Mixed strategies
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Matching Pennies
Example
A game is played between two players, player 1 and player 2. Each
player has a penny and must secretly turn the penny to head
Lecture 6
Extensive form games: Applications
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Extensive form games: Applications
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Stackelberg model of duopoly competition.
Stackelberg model of duopoly competition.
Two firms, 1 and 2, choose quantities.
The unit cost of production
ECON2112 Game Theory & Business Strategy
Week 9: Dynamic Games of Incomplete Info
Gabriele Gratton
Semester 1, 2016
Gabriele Gratton
ECON2112 Game Theory & Business Strategy Week 9: Dynamic Games of Incomplete Info
Bayes Nash equilibrium
static games of i
ECON2112 Game Theory & Business Strategy
Week 8: Applications of Bayes Nash Equilibrium
Gabriele Gratton
Semester 1, 2016
Gabriele Gratton
ECON2112 Game Theory & Business Strategy Week 8: Applications of Bayes Nash Equilibrium
Extending the Definition
we
ECON2112 Game Theory & Business Strategy
Week 10: PBE
Gabriele Gratton
Semester 1, 2016
Gabriele Gratton
ECON2112 Game Theory & Business Strategy Week 10: PBE
PBE 1 and 2
Requirement 1 [R1] At any information set, the player with the
move must have a beli
ECON2112 Game Theory & Business Strategy
Week 7: Games of Incomplete Information
Gabriele Gratton
Semester 1, 2016
Gabriele Gratton
ECON2112 Game Theory & Business Strategy Week 7: Games of Incomplete Information
Some logistics
consultation: Tuesday 3-5pm
Lecture 5
Extensive form games.
Subgame perfect equilibrium
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Extensive form games. SPE
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Introduction
In a normal form game, players take decisions simultaneously.
In an extensive form game, players take decisions sequentially.
A per
ECON2112 Game Theory & Business Strategy
Week 11: Signaling
Gabriele Gratton
Semester 1, 2016
Gabriele Gratton
ECON2112 Game Theory & Business Strategy Week 11: Signaling
Signaling
signaling games are a common class of dynamic games of
incomplete informat
Lecture 1
Normal form games and Nash equilibrium
ECON2112
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Normal form games and Nash equilibrium
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Course Structure
Lectures
Lecture notes will be available in the course website.
Most of the material is covered in: Game Theory for applied e
Game Theory and Business Strategy
Tutorial 11
Gary Liang
Semester 1, 2017
UNSW Australia
Agenda
Revision Questions
Stackelberg competition
Firm 1 and Firm 2 choose quantities 1 and 2 to produce. They face a marginal cost of
1 and 2 respectively. Assume 2