February 4th , 2016
ECON 451 Spring 2016
Econ 451 - Homework #2
Due: February 16, 2016
1. (35 points) Find all the (pure strategy) Nash equilibria for each of the following games.
(a) (5 points)
X
Y
U
0,4
4,0
M
3,3
3,3
D
4,0
0,4
Solution: No pure strategy
January 21st , 2016
ECON 451 Spring 2016
Econ 451 - Homework #1
Due: February 2, 2016
1. (20 points) For each of the following games and for each player determine which strategies are dominated.
(a) (5 points)
L
R
A
3,3
2,0
B
4,1
8,-1
(b) (5 points)
L
C
R
Econ 451 - Game Theory
Other Nash Equilibrium Illustrations: Bertrand and Hotelling
Jacopo Magnani
Purdue University
1 / 32
Bertrands Oligopoly Model
While in Cournots model, rms compete on quantity, in another
classical model by Bertrand, rms are assumed
Econ 45100 - Game Theory
Midterm #1
February 24, 2015
Time: 80 Minutes
120 Points Possible
First Name:
Last Name:
Class Time (circle one): 9:00 AM / 4:30 PM
Instructions:
DO NOT turn over your exam until you are told to do so.
This test contains 2 sectio
Econ 45100 - Game Theory
Midterm #2
March 31, 2015
Time: 80 Minutes
120 Points Possible
First Name:
Last Name:
Class Time (circle one): 9:00 AM / 4:30 PM
Instructions:
DO NOT turn over your exam until you are told to do so.
This test contains 2 sections:
ECON 451 - Game Theory
1
Purdue University - Fall 2015
Tuesdays and Thursdays 10:30AM or 1:30PM (RAWL 1057)
1
Course Description
Economics 451 is a course in game theory, a mathematical theory of interactions among decisionmakers. The goal of this class i
Econ 451 - Game Theory
Nash Equilibrium Illustrations: Cournots Oligopoly Model
Jacopo Magnani
Purdue University
1 / 24
Oligopoly
Competition between a small # of sellers.
2 / 24
Oligopoly
Basic economic theory (demand and supply analysis) focuses on
perf
Econ 451 - Game Theory
Best Response and Dominated Strategies
Jacopo Magnani
Purdue University
1 / 27
A Guessing Game
Lets play the following game!
Each of you has to pick an integer number between 0 and 100 (write
it on a piece of paper).
The winner of t
September 1st , 2015
ECON 451 Fall 2015
Econ 451 - Homework #1
Due: September 10, 2015
1. (10 points) Find all Nash Equilibria of the following game:
a
b
A 1,2
0,3
B 0,0
1,2
Solution: N E = (B, b)
2. (10 points) Find all Nash Equilibria of the following g
September 1st , 2015
ECON 451 Fall 2015
Econ 451 - Homework #1
Due: September 10, 2015
1. Find all Nash Equilibria of the following game:
a
b
A 1,2
0,3
B 0,0
1,2
2. Find all Nash Equilibria of the following game:
a
b
A 0,2
0,0
B 2,1
1,2
C 1,1
2,2
3. Find
Econ 451 - Game Theory
Introduction
Jacopo Magnani
Purdue University
1 / 18
Introducing myself
Prof. Jacopo Magnani
Oce: Krannert 362
Oce Hours: Wednesday 9:00-11:00 a.m.
Email: jmagnani@purdue.edu
2 / 18
What is game theory?
A mathematical theory of inte
Econ 451 - Game Theory
Strategic Games
Jacopo Magnani
Purdue University
1 / 21
The basic idea of a game, a situation of strategic interaction, is that
there are many decision-makers (called players) and the payo of a
player depends on the actions of all p
Econ 451 - Game Theory
Nash Equilibrium
Jacopo Magnani
Purdue University
1 / 12
Which actions will rational players choose
in a game?
The rst clear answer to this question was
formulated by John Nash (1928-2015).
Started as mathematics graduate student
at
Econ 451 - Game Theory
Nash Equilibrium in Games with Many Players
Jacopo Magnani
Purdue University
1 / 23
Voting
Stylized model of voting in the US Presidential election.
Players: there are D democrats and R republicans.
If a player votes, she votes for
ECON 451 - Game Theory
Purdue University - Spring 2015
Tuesdays and Thursdays 9:00AM (KRAN G018) or 4:30PM (RAWL 2070)
Course Website: http:/jnromero.com/courses/2015/ECON451/
1
Course Description
Economics 451 is a course in game theory. The main goal of
Economics of Information
(ECON3016)
Review of decision theory under uncertainty
Concavity and convexity
A function G ( x ) is:
-concave if G ( x ) ' 0
-strictly concave if G ( x) ' 0
-Convex if G ( x ) ' 0
-Strictly convex if G ( x) ' 0
Lets draw them in
Econ 451 - Game Theory
OLIGOPOLY
Jacopo Magnani
Purdue University
1 / 60
Oligopoly
Oligopoly: Competition between a small number of sellers.
2 / 60
Oligopoly
Basic economic theory (demand and supply analysis) focuses on
perfectly competitive markets.
A la
January 21st , 2016
ECON 451 Spring 2016
Econ 451 - Homework #1
Due: February 2, 2016
1. (20 points) For each of the following games and for each player determine which strategies are dominated.
(a) (5 points)
L
R
A
3,3
2,0
B
4,1
8,-1
Solution: Player 1:
Econ 451 - Game Theory
BASIC IDEAS
Jacopo Magnani
Purdue University
1 / 15
Example of a game
Consider the competition between two movies: Disneys A Bugs Life and
DreamWorks Antz, both released in the fall of 1998.
2 / 15
Example of a game
Timeline:
1
Idea
Econ 451 - Game Theory
Introduction to Econ 451
Jacopo Magnani
Purdue University
1 / 14
Introducing myself
Prof. Jacopo Magnani
Oce: Krannert 362
Oce Hours: Tuesdays and Thursdays 10:30 a.m.-12:30 p.m.
Email: jmagnani@purdue.edu
2 / 14
What is game theory
February 4th , 2016
ECON 451 Spring 2016
Econ 451 - Homework #2
Due: February 16, 2016
1. (35 points) Find all the (pure strategy) Nash equilibria for each of the following games.
(a) (5 points)
X
Y
U
0,4
4,0
M
3,3
3,3
D
4,0
0,4
(b) (5 points)
L
C
R
U
2,0
Econ 451 - Game Theory
BASIC IDEAS
Jacopo Magnani
Purdue University
1 / 15
Example of a game
Consider the competition between two movies: Disneys A Bugs Life and
DreamWorks Antz, both released in the fall of 1998.
2 / 15
Example of a game
Timeline:
1
Idea
ECON 451 - Game Theory
Purdue University - Spring 2016
Tuesdays and Thursdays 7:30AM or 9:00AM (Krannert Building G020)
1
Course Description
Economics 451 is a course in game theory, a mathematical theory of interactions among decisionmakers. The goal of
Econ 451 - Game Theory
DOMINANCE AND BEST RESPONSE
Jacopo Magnani
Purdue University
1/7
Dominated strategies
Denition
A pure strategy si of player i is dominated if there is another (pure or
mixed) strategy of player i, i , such that ui (i , si ) > ui (si
Econ 451 - Game Theory
RATIONALIZABILITY AND NASH EQUILIBRIUM
Jacopo Magnani
Purdue University
1/4
Iterated dominance
Iterated dominance procedure:
1
Delete all of the dominated strategies for each player. The strategies
that remain dene a new, reduce gam
ENGSC 2333 Thermodynamics
Chapter 3
3-1
Objectives
To apply the energy balance to a system of interest
requires knowledge of the properties of the system
and how the properties are related. The objective of
Chapter 3 is to introduce property relations rel
CPS 296.1
Extensive-form games
Vincent Conitzer
conitzer@cs.duke.edu
Extensive-form games with
perfect information
Player 1
Player 2
2, 4
Player 2
5, 3
Leaves of the tree show
player 1s utility first, then
player 2s utility
3, 2
1, 0
Players do not move
December 8th , 2015
ECON 451 Fall 2015
Econ 451 - Practice problems
1
Longer problems
Be able to show all the steps when solving the following exercises.
1. Consider a market where the inverse demand is P = 1200 Q. Firm 1 and rm 2 compete by setting their
December 8th , 2015
ECON 451 Fall 2015
Econ 451 - Practice problems
1
Longer problems
Be able to show all the steps when solving the following exercises.
1. Consider a market where the inverse demand is P = 1200 Q. Firm 1 and rm 2 compete by setting their