ORIE 4350: Assignment 1
Instructor: Krishnamurthy Iyer
September 5, 2014
Due on: September 12, 2014, 12pm
Please submit your homework in the dropbox in Rhodes 2nd oor lobby.
1. It is typically hard to come up with an individuals preference order that is n

ORIE 4350: Assignment 2
Instructor: Krishnamurthy Iyer
September 12, 2014
Due on: September 19, 2014, 12pm
Please submit your homework in the dropbox in Rhodes 2nd oor lobby.
1. Consider the game of Inverse Nim, where the player removing the last coin los

OR 4350: Introduction to Game Theory. Spring 2013.
Homework Set 5. Due: Noon, Wednesday March 13, in the dropbox outside the
main ORIE oce, Rhodes 206. Recall that this must be ONLY YOUR OWN WORK,
although you may discuss solution approaches with others.

ORIE 4350: Assignment 5
Instructor: Krishnamurthy Iyer
October 15, 2014
Due on: Oct 10, 2014, 12pm
Please submit your homework in the dropbox in Rhodes 2nd floor lobby.
1. Consider the following two player game between players I and II:
(a) Find

ORIE 4350: Assignment 3
Instructor: Krishnamurthy Iyer
September 19, 2014
Due on: September 26, 2014, 12pm
Please submit your homework in the dropbox in Rhodes 2nd oor lobby.
1. Consider the following bargaining game between two players. Players I and II

ORIE 4350: Assignment 1
Instructor: Krishnamurthy Iyer
September 14, 2014
Due on: September 12, 2014, 12pm
Please submit your homework in the dropbox in Rhodes 2nd oor lobby.
1. It is typically hard to come up with an individuals preference order that is

ORIE 4350: Assignment 4
Instructor: Krishnamurthy Iyer
September 26, 2014
Due on: October 3, 2014, 12pm
Please submit your homework in the dropbox in Rhodes 2nd oor lobby.
1. In class, assuming Axioms 1-4, we argued that if u1 is a von Neumann-Morgenstern

ORIE 4350: Introduction to Game Theory
Syllabus
Fall 2015
Course description:
In many real-life settings, a group of agents or decision makers interacts by each agent choos-
ing an action, and the actions chosen by every agent together determine the outc

Fall 2016
Game Theory (ORIE 4350)
Recitation 4
Mixed Strategy Nash Equilibria
1. Consider Rock-Paper-Scissors, where a player gets one dollar if they win, zero dollars if they
draw, and loses a dollar if they lose. Find all mixed-strategy Nash-Equilibria

Fall 2016
Game Theory (ORIE 4350)
Recitation 5
1. cfw_Tadelis 6.8 Market Entry: Three firms are considering entering a new market. The payoff
, where n is the number of firms that enter. The cost of entering
for each firm that enters is 150
n
is 62.
a. Fi

Fall 2016
Game Theory (ORIE 4350)
Recitation 1
1. In class we assumed that preference relations were both transitive and complete. Its clear why
we require completeness, but it may be less clear why we require transitivity. Consider the
following situatio

Fall 2016
Game Theory (ORIE 4350)
Recitation 6
Zero Sum Games
1. Define the matrix
1 4 9
A = 7 3 1 .
3 10 7
(a) Explicitly write out the maxmin linear program.
(b) Explicitly write out the minmax linear program.
(c) Write out the complimentary slackness c

Fall 2016
Game Theory (ORIE 4350)
Recitation 3
1. Cournot Equilibrium
In class we examined one of the classic models in game theory, Cournots model of duopoly. But
lets now go one step further.
Instead of two firms, suppose that there are N identical firm

ORIE 4350: Quiz 1
Instructor: Krishnamurthy Iyer
Thursday, September 29, 2016
1. Question 1 [5 points], (Lecture 2, p. 18)
Give a precise definition of a weakly dominated strategy.
0
Solution: A strategy si for player i is weakly dominated by si if
0
i (s

ORIE 4350: Assignment 6
Instructor: Krishnamurthy Iyer
October 17, 2014
Due on: October 24, 2014, 12pm
Please submit your homework in the dropbox in Rhodes 2nd oor lobby.
1. Consider the following two player game:
A
B
C
D
a
(1,2)
(0,1)
(1,2)
(0.5,1)
b
(4,

ORIE 4350: Assignment 5
Instructor: Krishnamurthy Iyer
October 3, 2014
Due on: Oct 10, 2014, 12pm
Please submit your homework in the dropbox in Rhodes 2nd oor lobby.
1. Consider the following two player game between players I and II:
a
b
c
d
A
(1,3)
(3,2)

OR 4350: Introduction to Game Theory. Spring 2013.
Homework Set 6. Due: Noon, Wednesday March 27, in the dropbox outside the
main ORIE oce, Rhodes 206. Recall that this must be ONLY YOUR OWN WORK,
although you may discuss solution approaches with others.

ORIE 4350, Spring 2013: Homework 5 Solutions
Problem 1 (Question 5.9.21)
(a)
1M = 1,000,000.
Eve
1M-1
1M-1
1M
1M-3
1M-1
1M+1
1M-1
Adam
1M+1
1M
1M-3
The Nash equilibrium is (1M-1, 1M-1).
This is a version of the Prisoners Dilemma since
Nash equilibrium giv

OR 4350: Introduction to Game Theory. Spring 2013.
Homework Set 7. Due: Noon, Wednesday April 3, in the dropbox outside the
main ORIE oce, Rhodes 206. Recall that this must be ONLY YOUR OWN WORK,
although you may discuss solution approaches with others. P

OR 4350: Introduction to Game Theory. Spring 2013.
Homework Set 8. Due: Noon, Wednesday April 10, in the dropbox outside the
main ORIE oce, Rhodes 206. Recall that this must be ONLY YOUR OWN WORK,
although you may discuss solution approaches with others.

ORIE 4350, Spring 2013: Homework 6 Solutions
Problem 1 (Question 6.9.29)
Cooperative payoff region is the convex hull of cfw_(4,2), (5,4), (2,5), (1,3).
Noncooperative payoff region:
Here, p is the probability that Player I chooses down and q is the proba

ORIE 4350, Spring 2013: Homework 7 Solutions
1 2
9 7
3 4 5
. Let () be Player Is expected payoff if he uses strategy 1
5 3 1
Problem 1 (Question 7.11.13)
Player Is payoff matrix =
with probability 1 , and strategy 2 with probability , and Player II uses

ORIE 4350, Spring 2013: Homework 8 Solutions
(a) When they payoff matrix in a zero s um game is , player I gets payoff of when he uses strategy and
player II uses strategy . Now suppose player I becomes player II and the payoff matrix is . If he still use

Fall 2014
Game Theory (ORIE 4350)
Recitation 1
Work in pairs and show the TA your work before you leave.
1. (Binmore p. 70 #1, parts (a) - (e) The gure below shows the tree of a stricly competitive
game G of perfect information without chance moves.
(a) H

ORIE 4350: Introduction to Game Theory
Syllabus
Fall 2014
Course description:
In this course, we consider situations such as follows:
1. How should Amazon, Apple, and Google price their tablets to maximize their prot, given that the
total demand depends o

Introduction to Game Theory
ORIE 4350
Instructor: Krishnamurthy Iyer
My Information
Location: 225 Rhodes Hall
E-mail: kriyer@cornell.edu
Web: http:/people.orie.cornell.edu/kriyer/
Office hours: Tue 2-3pm, Wed 12-1pm
Course Information
Class timing: Tue, T

Recitation 7
1. In the following game, what strategies survive iterated elimination of strictly dominated
strategies? What are the pure strategy Nash equilibria?
L
C
R
T
2, 0
1, 1
4, 2
M
3, 4
1, 2
2, 3
B
1, 3
0, 2
3, 0
Solution: Observe that T strictly do

ORIE 4350: Introduction to Game Theory
Syllabus
Fall 2016
Course description:
In many real-life settings, a group of agents or decision makers interacts by each agent choosing an action, and the actions chosen by every agent together determine the outcome

Fall 2016
Game Theory (ORIE 4350)
Recitation 2
Dominance Elimination
1. Two players (1 and 2) have a budget of 4 dollars each. They are bidding in an auction, where
$8 are being auctioned off. Each bids an amount xi cfw_0, 1, 2, 3, 4 dollars. Player i get

Fall 2016
Game Theory (ORIE 4350)
Recitation 7?
1. In the following game, what strategies survive iterated elimination of strictly dominated strategies? What are the pure strategy Nash equilibria?
L
C
R
T
2, 0 1, 1 4, 2
M
3, 4 1, 2 2, 3
B
1, 3 0, 2 3, 0
2