PSC/ECO 288
Game Theory
Prof. Tasos Kalandrakis
Spring 2016
Assignment #6: Due in class Wednesday, April 6
Please write clearly and make sure to justify all your answers.
1. (25 points total) Consider the following game in strategic form
Player 1
E
C
N
E
Lecture 18, 3/28
Bayesian games.
Bayesian Nash equilibrium.
Material covered:
Osborne, Sections 9.1-9.2.
Uncertainty in Games
Up to now we have only considered games with
complete information.
Strategies and payoffs are common knowledge
But this ass
Lecture 19, 4/2
More on Bayesian games.
Bayesian Games
Set of players, N.
Set of actions Ai for each player i.
Set of types Ti for each player i.
Prior probability of a type profile t given by p(t).
A payoff function, ui(a; t), for each profile of
a
Lecture 16, 3/21
Games of Imperfect Information
Nash equilibrium
Subgames & SPNE
Behavioral strategies
Material covered:
Osborne, Sections 7.1 and 10.1-10.3 (ignore
material on moves by Chance)
Nash Equilibrium in Games with
Imperfect Information
A
Lecture 3, 1/25
More implications of rationality
Strictly dominated actions
Common knowledge and iterated elimination
Weakly dominated actions
Related Reading:
Osborne, chapter 2, section 2.9.
Optional: Osborne, chapter 12, section 12.2-4
(relies on mat
Lecture 4, 1/27
Nash equilibrium
Properties & interpretation
Nash equilibrium and dominated strategies
Related Reading:
Osborne, chapter 2, sections 2.6, 2.7, 2.9.
Recap
Last time, we sought implications of rationality for
behavior in games.
We conc
Lecture 5, 2/1
Finding Nash equilibria
n-player stag hunt
Binary voting
Related Reading
Osborne, chapter 3, section 3.3.
Nash Equilibrium
A Nash equilibrium is a profile of action choices
such that no individual wishes to change her action
given what
Lecture 7, 2/8
Conclusion of War of Attrition & best responses
Mixed Strategies & Preferences over lotteries
Nash equilibrium in mixed strategies
Related Reading
Osborne, chapter 4, section 4.1, 4.2, 4.3, 4.12.
Nash Equilibrium II
Profile a* is a Nash
Lecture 6, 2/3
Electoral Competition
Best Responses & Nash Equilibrium
War of Attrition
Common project
More Electoral Competition?
Related Reading
Osborne, chapter 2, section 2.8.
Osborne, chapter 3, sections 3.3-3.4.
Electoral Competition
Set of
PSC/ECO 288
Game Theory
Prof. Tasos Kalandrakis
Spring 2016
Assignment #1: Due in class Wednesday, February 3
Please write clearly and make sure to justify all your answers.
1. (11 points total) For the following game in strategic form:
Player 1
U
UM
DM
D
PSC/ECO 288
Game Theory
Prof. Tasos Kalandrakis
Spring 2016
Assignment #2: Due in class Wednesday, February 10
Please write clearly and make sure to justify all your answers.
1. (13 points total) Consider a two-player divide-the-dollar game with
the follo
PSC/ECO 288
Game Theory
Prof. Tasos Kalandrakis
Spring 2016
Assignment #3: Due in class Wednesday, February 17
Please write clearly and make sure to justify all your answers.
1. (10 points total) Two people can perform a task if, and only if,
they both ex
PSC/ECO 288
Game Theory
Prof. Tasos Kalandrakis
Spring 2016
Assignment #4 answer key
1. The game tree below represents the extensive form.
1
C
D
2
E
2, 1
2
F
G
4, 3
H
3, 4
The equivalent strategic form is
C
D
2
EH
2, 1
1, 2
EG
2, 1
3, 4
FG
4, 3
3, 4
FH
4,
PSC/ECO 288
Game Theory
Prof. Tasos Kalandrakis
Spring 2016
Assignment #5 answer key
1. There are two important general points about this problem. First,
in comparing payo from accepting an oer versus rejecting it, it is
important to consistently account
Lecture 17, 3/26
Exiting a declining industry.
Equilibrium price in a market game.
Material covered:
Osborne, Sections 7.5
Exit from a declining industry
Two firms i = 1, 2, are present in an industry in
which consumer demand is declining over time.
Lecture 13, 3/5
Backward Induction
Ultimatum Bargaining
The Holdup Problem
Centipede Game
Material covered:
Osborne, Sections 6.1.
Backward Induction
In games of perfect information, backward
induction identifies all (pure strategy) subgame
perfect Nash
Lecture 14, 3/7
Centipede Game
Zero-sum games and perfect information
Zermelos Theorem
Material covered:
Osborne, Sections 11.3-11.4.
The Centipede Game
Imagine two piles of money on a table. The large
pile has $10 and the small pile has 10.
Player
PSC/ECO 288
Game Theory
Prof. Tasos Kalandrakis
Spring 2016
Assignment #8: Due in class Wednesday, April 20
Please write clearly and make sure to justify all your answers.
1. (25 points total) Find a WSE in the following dynamic game of
incomplete informa
PSC/ECO 288
Game Theory
Prof. Tasos Kalandrakis
Spring 2016
Assignment #7: Due in class Wednesday, April 13
Please write clearly and make sure to justify all your answers.
1. (13 points total) For the following Bayesian game, assume both
players beliefs a
PSC/ECO 288
Game Theory
Prof. Tasos Kalandrakis
Spring 2016
Assignment #9: Due in class Wednesday, April 27
Please write clearly and make sure to justify all your answers.
1. (25 points total) Consider the Sir Philip Sydney game (thus named
by evolutionar
Lecture 2, 1/23
Games in strategic form
Material covered:
Osborne sections 2.1 to 2.5 and 17.1 to 17.4
Games in Strategic Form
A game in strategic form can be formally defined
by:
A set of players.
A set of actions (strategies), available to each
pla
Lecture 4, 1/30
Common knowledge of actions
Nash equilibrium
Examples of Nash equilibria
Solving for Nash equilibria
Material covered:
Osborne sections 2.6 and 2.7
More Common Knowledge
We have seen that common knowledge of
rationality (and of payoffs)
Lecture 3, 1/25
Consequences of rationality
Dominant actions
Strictly dominated actions
Iterated elimination
Weakly dominated actions
Material covered:
Osborne sections 2.9 and 12.2 to 12.4 (beware!)
Rational play in PD
Player 2
Cooperate Defect
Cooperat
Lecture 5, 2/1
Nash equilibrium and rationality
n-player stag hunt
n-player binary voting
Electoral Competition
Material covered:
Osborne, Sections 2.7, 2.9 and 3.3.
Nash equilibrium & rationality
What is the relationship between dominance and
Nash equi
PSC/ECO 288: GAME THEORY
Prof. Mark Fey
Lecture 1, 1/18
Overview
Logistics
Games
A game is any situation in which two or more
individuals make choices from some menu of
actions and such that each individuals welfare
depends on the choices of others (as
Lecture 6, 2/6
Electoral Competition
Best Responses & Nash Equilibrium
War of Attrition
Common project
Material covered:
Osborne, Sections 2.8, 3.3 and 3.4.
Median Voter Theorem
In two candidate electoral competition,
with a one-dimensional policy
Lecture 11, 2/27
Games in the Extensive Form
Strategies
Material covered:
Osborne, Sections 5.1-5.2.
Sequential Choice
To this point, we have only considered
simultaneous choice.
But many games involve sequential choice.
Policy-making: laws, regulat
Lecture 12, 2/29
Strategy
Nash equilibrium in extensive form games
Subgame perfect Nash equilibrium
Material covered:
Osborne, Sections 5.2-5.5.
Extensive Form (Perfect Information)
A set of players:
N = cfw_1, 2, , n.
A game tree
o1
h2
o2
h1
h3
o4