6.254 Game Theory with Engr App
Midterm
Thursday, April 8, 2010
Problem 1 (35 points) For each one of the statements below, state whether it is true or false. If the answer
is true, explain why. If the answer is false, give a counterexample. Explanations
6.254 Game Theory with Engineering
Applications
Midterm
April 8, 2008
Problem 1 : (35 p oints) Consider a game with two players, where the
pure strategy of each player is given by xi [0, 1]. Assume that the payo
function ui of player i is given by
ui (x1
6.254 Game Theory with Engineering
Applications
Midterm
April 11, 2006
Problem 1 : (35 p oints) Consider a Bertrand competition between two
rms, where each rm chooses a price pi [0, 1]. Assume that one unit of
demand is to be split between the two rms. Th
6.972 Game Theory and Equilibrium Analysis
Midterm Exam
April 6, 2004; 1-2:30 pm
Problem 1. (40 points) For each one of the statements below, state whether
it is true or false. If the answer is true, explain why. If the answer is false, give a
counterexam
6.254 : Game Theory with Engineering Applications
Lecture 8: Supermodular and Potential Games
Asu Ozdaglar
MIT
March 2, 2010
1
Game Theory: Lecture 8
Introduction
Outline
Review of Supermodular Games
Potential Games
Reading:
Fudenberg and Tirole, Section
6.254 : Game Theory with Engineering Applications
Lecture 7: Supermodular Games
Asu Ozdaglar
MIT
February 25, 2010
1
Game Theory: Lecture 7
Introduction
Outline
Uniqueness of a Pure Nash Equilibrium for Continuous Games
Supermodular Games
Reading:
Rosen J
6.254: Game Theory with Engineering Applications February 23, 2010
Lecture 6: Continuous and Discontinuous Games
Lecturer: Asu Ozdaglar
1
Introduction
In this lecture, we will focus on:
Existence of a mixed strategy Nash equilibrium for continuous games
6.254 : Game Theory with Engineering Applications
Lecture 6: Continuous and Discontinuous Games
Asu Ozdaglar
MIT
February 23, 2010
1
Game Theory: Lecture 6
Introduction
Outline
Continuous Games
Existence of a Mixed Nash Equilibrium in Continuous Games
(Gl
6.254 : Game Theory with Engineering Applications
Lecture 5: Existence of a Nash Equilibrium
Asu Ozdaglar
MIT
February 18, 2010
1
Game Theory: Lecture 5
Introduction
Outline
Pricing-Congestion Game Example
Existence of a Mixed Strategy Nash Equilibrium in
6.254: Game Theory
February 11, 2010
Lecture 4: Correlated Rationalizability
Lecturer: Asu Ozdaglar
1
Correlated Rationalizability
In this note, we allow a player to believe that the other players actions are correlated in
other words, the other players m
6.254 : Game Theory with Engineering Applications
Lecture 4: Strategic Form Games - Solution Concepts
Asu Ozdaglar
MIT
February 11, 2010
1
Game Theory: Lecture 4
Introduction
Outline
Review
Correlated Equilibrium
Existence of a Mixed Strategy Equilibrium
6.254 : Game Theory with Engineering Applications
Lecture 3: Strategic Form Games - Solution Concepts
Asu Ozdaglar
MIT
February 9, 2010
1
Game Theory: Lecture 3
Introduction
Outline
Review
Examples of Pure Strategy Nash Equilibria
Mixed Strategies and Mix
6.254 : Game Theory with Engineering Applications
Lecture 2: Strategic Form Games
Asu Ozdaglar
MIT
February 4, 2009
1
Game Theory: Lecture 2
Introduction
Outline
Decisions, utility maximization
Strategic form games
Best responses and dominant strategies
D
6.254 : Game Theory with Engineering Applications
Lecture 1: Introduction
Asu Ozdaglar
MIT
February 2, 2010
1
Game Theory: Lecture 1
Introduction
Optimization Theory: Optimize a single objective over a decision
variable x Rn .
i ui ( x )
subject to x X R
6.254 Game Theory with Engr App
Problem Set 5
Due: Thursday, April 29, 2010
Problem 1 (Three player game)
Consider the following game with three players. Player 1 chooses row; player 2 chooses column; and player
3 chooses matrix.
P1 \ P2
U
D
L
1, 1, 1
0,
6.254 Game Theory with Engr App
Problem Set 4
Due: Thursday, April 1, 2010
Problem 1 (Subgame perfect equilibria)
(a) [Dictator game and impunity game] The dictator game differs from the ultimatum game only in
that person 2 does not have the option to rej
6.254 Game Theory with Engr App
Problem Set 3
Due: Thursday, March 18, 2010
Problem 1 (Supermodular Games) Are the two games below supermodular?
P1 \ P2
A
B
C
A
0, 0
1, 0
2, 4
B
0, 1
1, 1
1, 1
C
4, 2
1, 1
2, 2
P1 \ P2
A
B
C
A
0, 0
1, 4
0, 0
B
0, 3
2, 2
4,
6.254 Game Theory with Engr App
Problem Set 2
Due: Thursday, March 4, 2010
Problem 1 (Existence of Pure Strategy Nash Equilibrium)
Note that a function ui (s) is upper semi-continuous at s, if, for any sequence sn converging to s,
lim supn ui (sn ) ui (s)
6.254 Game Theory with Engr App
Problem Set 1
Due: Thursday, February 18, 2010
Problem 1 (Iterated Elimination of Strictly Dominated Strategies)
Consider the iterated elimination of strictly dominated strategies in the strategic form game I , (Si )i I , (