LECTURE 9
Readings: Section 3.4-3.5
Lecture outline
PDF: Review
Multiple random variables
Conditioning
Independence
Examples
Continuous r.v.s and PDFs
Summary of Concepts
Joint PDF
Interpretation:
Expectation:
(1)
Joint PDF
(2)
From the joint to
LECTURE 8
Readings: Section 3.1-3.3
Lecture outline
Probability density functions
Cumulative distribution functions
Normal random variables
Continuous Random Variables
Probability Density Function (PDF)
Means and Variance
Example: Uniform PDF
Cumulati
LECTURE 7
Readings: Finish Chapter 2
Lecture outline
Joint PMFs
Independent random variables
More expectations, variances
Binomial distribution revisited
The hat problem
Application: Point-to-Point
Communication
Review
Random Variables and PMF
Expectat
LECTURE 6
Readings: Sections 2.4-2.6
Lecture outline
Review PMF, expectation, variance
Conditional PMF
Geometric PMF
Total expectation theorem
Joint PMF of two random variables
Independence
Review
Random variable X: function from
sample space to the rea
LECTURE 5
Readings: Sections 2.1-2.3, start 2.4
Lecture outline
Random variables
Probability mass function (pmf)
Binomial Random Variable
Expectation
Example
Random Variables - 1
An assignment of a value (number) to
every possible outcome.
Mathema
LECTURE 4
Readings: Sections 1.6
Lecture outline
Principles of counting
Many examples
Binomial probabilities
Discrete Uniform Law
Let all sample points be equally likely.
Then,
Just count
Basic Counting Principle
r steps
ni choices at step i
Num
LECTURE 2
Readings: Sections 1.3, 1.4
Lecture outline
Review
Conditional Probability
Three important tools:
Total probability theorem
Bayes rule
Multiplication rule
Example 0: Radar
Radar device, with 3 readings:
Low (0), Medium (?), High (1)
Pr
6.041: Probabilistic Systems Analysis
6.431: Applied Probability
Prof. Munther A. Dahleh
Course Outline
Introductions
Recitation Assignment
Tutorial Assignment
Text Book
Introduction to
Probability: Bertsekas
and Tsitsiklis
Grading Policy:
Q1: 25%,
Q2
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
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
6.972 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
Programming Examples
Example-3:
Taylor Series
Level : Easy
Program Problem Statement
Taylor series is a representation of a function as an
infinite sum of terms calculated from the values of its
derivatives at a single point i.e., it is a series expansio
Programming Examples
Name of the Program: String Division
Level : Difficult
String Division
Write a program which reads a string from the user and divides the
string into different classes such as Strings, Numbers and
AlphanumericStrings etc. Create all
Programming Example
Name of the Program: CGPA Calculation
Level : Easy
CGPA
Write a program to calculate the CGPA got by a
student. CGPA will be calculated on the basis of SGPA
and number of semester.
CGPA, which is the cumulative grade point average is
c
Programming Example
Name of the Program: Cell Phone Usage
Level : Easy
Cell Phone Usage
One cell phone service provider, launched the
following plan for SMS. For every user, 100 SMS are
free for each recharged talk time.
Write a program to calculate t
Programming Example
Name of the Program: Body Mass Index
Level : Easy
Body Mass Index
Body mass index (BMI) or Quetelet Index is a
statistical measure of the weight of a person scaled
according to height.
Body Mass Index is defined as the individual's b
Programming Examples
Example-4:
Black Jack
Level : Easy
Program Problem Statement
Blackjack is a very well known gambling card game played against a
dealer in a casino. In this card game, each player is trying to beat
the dealer, by obtaining a sum of car
Programming Examples
Example-2:
Banker's Algorithm
Level : Medium
Banker's Algorithm- Program Problem Statement
The Banker's algorithm is an algorithm developed for resource allocation
and to avoid deadlocks. The Banker's algorithm is run on the operating
Game Theory Simulation Projects
Simulate Spatial Pattern Formations in eg The Prisoners Dilemma
Prof Ken Hawick
k.a.hawick@massey.ac.nz, www.massey.ac.nz/~kahawick/student-projects.html
The so-called Prisonners Dilemma game involves two prisoners held in
Proceedings of the International Congress of Mathematicians
Hyderabad, India, 2010
Algorithms, Graph Theory, and Linear Equations in Laplacian Matrices
Daniel A. Spielman
Abstract. The Laplacian matrices of graphs are fundamental. In addition to facilitat
Representation and Learning in Computational Game Theory
Michael Kearns
University of Pennsylvania
Michael L. Littman
Rutgers University
Robert Schapire
Princeton University
Manfred K. Warmuth
U.C. Santa Cruz
February 11, 2003
A
PROJECT SUMMARY
Game theor
Economics, Game Theory and
Computer Science
Krzysztof R. Apt
CWI and University of Amsterdam
Economics, Game Theory and Computer Science p.1/22
Warning about Grand Challenges
AI.
Fifth Generation Project.
Iraq.
.
Economics, Game Theory and Computer Scienc
CPS 270: Artificial Intelligence
http:/www.cs.duke.edu/courses/fall08/cps270/
Game Theory
Instructor: Vincent Conitzer
2/3 of the average game
Everyone writes down a number between 0 and 100 Person closest to 2/3 of the average wins Example:
A says 50 B
Game Theory
Theodore L. Turocy Texas A&M University Bernhard von Stengel London School of Economics
CDAM Research Report LSE-CDAM-2001-09 October 8, 2001
Contents
1 What is game theory? 4 6 8 12 17 22 29 33 34 38 2 Denitions of games 3 4 5 6 7 8 Dominance
Introduction to the AI Magazine Special Issue on
Algorithmic Game Theory
Edith Elkind
Kevin Leyton-Brown
Abstract
We briey survey the rise of game theory as a topic of study in articial
intelligence, and explain the term algorithmic game theory. We then d
An Algorithmic Game Theory Primer
Tim Roughgarden
June 21, 2008
Abstract
We give a brief and biased survey of the past, present, and future of research on the interface
of theoretical computer science and game theory.
1
Introduction
By the end of the 20th
Game Theory
Themes
1. Introduction to Game Theory
2. Sequential Games
3. Simultaneous Games
4. Conclusion
Introduction to Game Theory
Game theory is the branch of decision theory concerned with interdependent decisions.
The problems of interest involve mu