Econ 106G Spring 2013
Homework 1: Dominated Stratgies, Best Responses
The due date for this homework is Monday April 15th in class.
1. Game Theory Concepts, True-False: For each of the following statements, state
whether it is true or false. If it is fals
Econ 106G Spring 2014
Solution to Final
1. Game Theory Concepts, True or False: Answer if the following statements are true or false. If they are false, give an example that contradicts
the statement.
(a) Every nite extensive form game with no simultaneou
Lecture 7 - Mixed Strategies
Econ 106G Spring 2013
Mixed Strategies and Mixed Strategy Nash Equilibrium
We have seen many examples of games where Nash equilibria (in pure strategies) exist, e.g.
the Prisoners Dilemma, Cournot competition etc. However, the
Econ 106G Spring 2013
Homework 2: Applications of Nash Equilibrium
The due date for this assignment is Monday April 29th in class.
1. Pure and Mixed Strategy Nash Equilibria: For all of the following games, draw the bestresponse functions in (p; q )-space
Econ 106G Spring 2013
Answers to Practice Problems 1: Basic Concepts, Dominated
Strategies
1
Basic Concepts
Fiscal cli sex-ratio and PrisonersDilemma are games of complete in,
formation. Pre-existing conditions in Health Insurance Markets is a game
of inc
Econ 106G Spring 2016
Homework 2: Applications of Nash Equilibrium
The due date for this assignment is Friday April 29th in sessions.
1. Protecting LAZ: LAZ airport has a domestic and a international terminal but only one security team
(player 1) that can
Econ 106G Spring 2013
Practice Problems 1: Basic Concepts, Dominated Stratgies
You do not need to submit answers to these problems. I still encourage you to
think them through thoroughly, write down your answers and discuss them with
your classmates.
1. B
Lecture 10 - Extensive Form Games and Backward Induction
Watson - 14-15
Econ 106G Spring, 2016
Extensive Form Games and Game Trees
In many situations, players move sequentially, for example,
real games: chess, checkers, poker, go, nim,
in sports: chess,
Lecture 7 - Nash Equilibria: Cournot & Bertrand Competition
Watson - 10
Econ 106G Spring 2016
If firms are small compared to the market we usually assume that they take prices as
given. Thus when they decide on the quantities they produce or whether to en
Lecture 6 - Nash Equilibrium
Watson 9
Econ 106G Spring, 2016
Coordination and Anti-Coordination Games
Coordination
Two friends have gone to Disneyland together and lost each other there. There are two focal
points to meet, the Matterhorn or Space Mountain
Lecture 2 - Dominance and Best Responses
Watson: 3-6
Econ 106G Spring, 2015
What is Game Theory?
Game theory is a tool to analyze interaction among a group of rational, strategic agents.
Definition 1 A Normal Form Game is defined by
1. Players: i 2 cfw_1,
Lecture 7 - Nash Equilibria: Cournot & Bertrand Competition
Watson - 10
Econ 106G Spring 2016
If rms are small compared to the market we usually assume that they take prices as
given. Thus when they decide on the quantities they produce or whether to ente
Econ 106G Spring 2015
Solutions to Practice Problems 3: Applications of Normal Form Games
1. Game Theory Concepts, True or False: Answer if the following statements are
true or false. If they are false, give an example that contradicts the statement
(a) E
Econ 106G Spring 2015
Solution to Homework 2: Applications of Nash Equilibrium
1. Protecting LAZ: LAZ airport has a domestic and a international terminal but only one security team
(player 1) that can cover only one of the terminals. A terrorist organizat
Lecture 8 - Mixed Strategies
Watson - 11
Econ 106G Spring 2016
Mixed Strategies and Mixed Strategy Nash Equilibrium
We have seen many examples of games where Nash equilibria (in pure strategies) exist, e.g.
the Prisoners Dilemma, Cournot competition etc.
Lecture 11 - Commitment
Watson 15-16
Econ 106G Spring 2016
Commitment
War Game - Chicken
Consider the interaction between two armies. Each army can either F ight or Retreat. Each
army prefers to fight if the other retreats but prefers to retreat if the ot
Econ 106G Spring 2015
Practice Problems 5
1. The Final Exam: When a professor is giving an exam, his utility decreases in
the eort it takes him to make up new questions but he also cares about how
students learn and pass the class (see below). He has two
Econ 106G Final, Spring 2014
Moritz Meyer-ter-Vehn
1. Game Theory Concepts, True or False: Answer if the following statements are
true or false. If they are false, give an example that contradicts the statement.
(a) Every nite extensive form game with no
Econ 106G Spring 2015
Solution to Assignment 3: Extensive Form Games
The due date for this assignment is Monday May 18th.
1. Game Theory Concepts, True or False: Answer if the following statements are
true or false. If they are false, give an example that
Econ 106G Spring 2015
Solutions for Assignment 4: Extensive Form Games
1. Game Theory Concepts, True or False: Answer if the following statements
are true or false. If they are false, give an example that contradicts the statement!
(a) If a symmetric stag
Econ 106G Spring 2015
Solutions to Practice Problems 5
1. The Final Exam: When a professor is giving an exam, his utility decreases in
the eort it takes him to make up new questions but he also cares about how
students learn and pass the class (see below)
Lecture 3 - Rationalizability
Watson: 7
Econ 106G Spring, 2016
A Beauty Contest
Each student chooses a number between 1 and 100. The student whose number is closest to
2/3 of the average of the chosen numbers wins the game.
I: 106G students
Si = f1;
; 100
Lecture 2 - Dominance and Best Responses
Watson: 3-6
Econ 106G Spring, 2015
What is Game Theory?
Game theory is a tool to analyze interaction among a group of rational, strategic agents.
Denition 1 A Normal Form Game is dened by
1. Players: i 2 f1; 2; 3;
Lecture 1 - Some Games
Watson: 1,2
Econ 106G Spring 2016
Some Games
Graccident
The EU (and the ECB and the IMF) bailed out Greece in 2010 and 2012 in return for
austerity measures
These austerity measures are highly unpopular in Greece and radical parties
Lecture 4 - Weak Dominance
Watson: 6
Econ 106G Spring, 2016
A Referendum
The citizens of a village have the chance to participate in a referendum. If the referendum
succeeds, i.e. more than 50% of the citizens participate (and vote for it), a policy is ch
Econ 106G Spring 2016
Solution to Homework 1: Dominated Stratgies, Best Responses
1. True-False:
(a) False. Cooperate is not a best response to any beliefs in the prisonersdilemma.
(b) True.
(c) False. In the beauty contest, all strategies si 2 f68; : : :
Econ 106G Spring 2016
Midterm Prep
1. Basic Concepts: For each of the games introduced in the rst lecture, determine
(a) whether we represented the game as an extensive-form game or as a normal-form
game
(b) whether or not the game is of complete informat
Econ 106G Spring 2016
Answers to Midterm Prep
Ex. 1-2.
Sex-ratio, PrisonersDilemmaand Run or Passare games of complete
information. In Crying it out the father has incomplete information about
the motivation of his daughter. Graccidentis a game of complet
Lecture 14 - Cooperation through Repeated Interaction
Watson: 22
Econ 106G Spring 2016
The dilemma of the prisoners has it roots in the divergence of individual interests, to play
Def ect, and the social interests, to both play Cooperate. The stark predic
Lecture 5 - Weak Dominance and Pivot Mechanisms
Watson: Econ 106G Spring, 2017
Abstract Allocation problem
Think about the following abstract allocation problem. You have as given the following:
Set of physical allocations, fx1 ; :; xM g
Group of players
Econ 106G Spring 2017
Homework 2: Applications of Nash Equilibrium
The due date for this assignment is Friday April 29th in sessions.
1. First price auction: In class, we studied the so-called second-price auction and argued that it is a
convenient model
Econ 106G Spring 2017
Homework 1: Dominated Stratgies, Best Responses
The due date for this homework is Friday April 21st in section.
1. Game Theory Concepts, True-False: For each of the following statements, state
whether it is true or false. If it is fa