Recap
Stochastic Games
Bayesian Games
Stochastic Games and Bayesian Games
CPSC 532A Lecture 13
October 24, 2006
Stochastic Games and Bayesian Games
CPSC 532A Lecture 13, Slide 1
Recap
Stochastic Games
Bayesian Games
Lecture Overview
Recap
Stochastic Games
Recap
Maxmin and Minmax
Linear Programming
Computing
Fun Game
Domination
Minmax and Dominance
CPSC 532A Lecture 6
September 28, 2006
Minmax and Dominance
CPSC 532A Lecture 6, Slide 1
Recap
Maxmin and Minmax
Linear Programming
Computing
Fun Game
Domination
Game Theory
Tutorial 3
Answers
Exercise 1 (Duality Theory) Find the dual problem of the following L.P.
problem:
max x0 = 3x1 + 2x2
s.t.
5x1 + 2x2 10
4x1 + 6x2 24
x1 + x2 1
(1)
x1 + 3x2 = 9
x1 0.
Solution : We are going to use rules (1),(2) and (3) from yo
Game Theory
Tutorial 2
Answers
Exercise 1 (Minimax problem) Three linear functions y1 , y2 and y3 are
dened as follows:
y1 = 2 x1 ,
y2 = x1 1,
y3 = 2x1 6.
Find
min max cfw_yi .
x
i=1,2,3
(1)
Solution : A way to solve problem (1) is to introduce an auxilia
Game Theory
Tutorial 3
Questions
Exercise 1 (Duality Theory) Find the dual problem of the following L.P.
problem:
max x0 = 3x1 + 2x2
s.t.
5x1 + 2x2 10
4x1 + 6x2 24
x1 + x2 1
(1)
x1 + 3x2 = 9
x1 0.
Exercise 2 (Free Variables) Solve the following problem:
m
GT (2003) 1
GAME THEORY (GT)
Thus far, we have considered situations where a single DM chooses an optimal decision without
reference to the effect his decision has on other DM's and without reference to the effect the decision of others
may have on him. A
Game Theory
Tutorial 2
Questions
Exercise 1 (Minimax problem) Three linear functions y1 , y2 and y3 are
dened as follows:
y1 = 2 x1 ,
y2 = x1 1,
y3 = 2x1 6.
Find
min max cfw_yi .
x
i=1,2,3
(1)
Exercise 2 (Minimax problem again) Find x1 , x2 satisfying
x1
Ith'f tr9cuy6 i~F
e
6
6
A fl't f 9 etwnt
f
l$0'iho|ntw iwYcfw_uhi tTlo ijf'hc t'cfw_oyfwGifd'hinwhh k 40i 'h kwdf ht66|2urhilf 0Go 'uc yfjfywti'!yfh w
2 u6 ehkh
d
en
PI 2
cfw_yiwYt n l
h
r6c!jifh tw
Y y$w9kw 'hjfif28ythng 'jfett$f 6tri
Duality Theory
Berc Rustem
November 23, 2010
Contents of this Lecture
Weak and Strong Duality, Complementary Slackness
Denition: Primal and Dual Problem
Weak and Strong Duality
Complementary Slackness
Obtaining the Dual of a Linear Program
Indirect and Di
Game Theory
Tutorial 1
Answers
Exercise 1 The manager of a multinational company and the union of workers are preparing to sit down at the bargaining table to work out the details
of a new contract for the workers. Each side has developed certain proposal
Game Theory
Tutorial 1
Questions
Exercise 1 The manager of a multinational company and the union of workers are preparing to sit down at the bargaining table to work out the details
of a new contract for the workers. Each side has developed certain propos
Game Theory, Spring 2014
Midterm Solutions
You have two hours to complete this exam. Please answer the following three questions.
Be sure to allocate your time in proportion to the points. Always justify your answers by
providing a formal proof or a detai
Game Theory, Spring 2014
Midterm Exam
Dino Gerardi
April 9th
You have two hours to complete this exam. Please answer the following three questions.
Be sure to allocate your time in proportion to the points. Always justify your answers by
providing a forma