Nash
Equilibrium:
Theory
Strategic or Simultaneous-move
Games
Definition: A simultaneous-move game
consists of:
A set of players
For each player, a set of actions
For each player, a preference rela
(a)
(b)
1
HG1M11
Sample question
Find the indefinite integral
1
Using integration by parts, or otherwise, find the indefinite integral
[ You may find it useful to note that
=
2.
a)
= ]
and
Evaluate
HG1M11
Engineering Mathematics 1
Problem Sheet 10
Find the following:1.
2
( x + sin x
1 1
+ )dx
x x3
1
2.
(1 2 x)
8
dx
1
1
2
3.
x
2
cos xdx
4.
cos 4 xdx
e x dx
6.
cos x sin
8.
x +1
dx
2
x + 2x
Vnble^ shefi1
b -Y. '
' t-
l+
DY
la
c.
g
Z c -os x
a
J ?C
do
6 t - -5 _ L *
-I
+ . 5 ehx -
b.
lD 6L*
A
Z
-6
2-t (3x + z)
2.a.
z
c,
3ec L
b &nz
- 6r)
+ . (zt + z)qi.,'-+)t(rbx
Stn Zx-
os 7*
- 9
2.
2
h.
HG1M11
1.
Engineering Mathematics 1
Problem Sheet 9
Sketch the following curves:(a)
(b)
y = (x 1)(x + 1)3
(c)
y = x(x 2)(x 4)
(d)
2.
y = x2(x 1)(2x + 3)
y = 2(x + 2)(x 1)2.
For each of the following f
4roblen shecf L
I a.
cfw_ -t r) : -t o
b.
+(-l)'-|
(t+I . 6
x=+lT
-J3'
c
- to6
d
g
- l o <tJg L
a.
X:l
b.
x - - 3 , 7 ,-L
c.
aJx, ro-a) nwn]ry'r excqt
d.
cfw_(*\ o
.+
-2r2, 3
g = frr) = *-zr-t = 1v -,
H61ICP-E1
The University of Nottingham
Malaysia Campus
DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING
A LEVEL 1 MODULE, SPRING SEMESTER 2011-2012
INTRODUCTION TO COMPUTER ENGINEERING
Time allowed
Repeated
Games
Repeated Prisoners
Dilemma
Thus far we have studied games, both static and dynamic,
which are only played once. We now move to an
environment where players interact repeatedly.
Each p
Nash
Equilibrium:
Illustrations
Cournots Model of Oligopoly
Single good produced by n firms
Cost to firm i of producing qi units: Ci(qi), where
Ci is nonnegative and increasing
If firms total outpu
Extensive Form
Games
With Perfect
Information
(Extensions)
Allowing for Simultaneous
Moves
New type of game where players make simultaneous decisions in a
sequential environment.
For example, player I
Extensive Form
Games
With Perfect
Information
(Theory)
Extensive Form Games with
Perfect Information
Entry Game: An incumbent faces the possibility of
entry by a challenger. The challenger may enter
o
The Theory
of Rational
Choice
The Theory of Rational Choice
A rational decision-maker chooses the best
action according to her preferences, among
the actions available to her.
Set of available actions
H61ICP-E1
The University of Nottingham
Malaysia Campus
DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING
A LEVEL 1 MODULE, AUTUMN SEMESTER 2012-2013
INTRODUCTION TO COMPUTER ENGINEERING
Time allowed
THE EIGENVALUE
PROBLEM
The Eigenvalue Problem
Eigenvalue problem arise in many situation,
for example
!Calculating the natural frequencies of
oscillation of a vibrating system
!Finding principal axes
HG1M11
1.
2.
2 3 x 2 1 x 6
Let f(x) =
.
otherwise
5
(a)
Find f(2), f(7), f(-1).
(b)
For what values of x is f(x) = 0?
(c)
If the domain of this function is cfw_x : x is real,sketch the graph of f
(d
MM1SM1 Mechanics of Solids 1
Chapter 5: Torsion
S1: Shear Stresses in Torsion
S2: Polar 2nd Moment of Area,
S3: Power Transmission
S4: Torque & Coupling in Shaft
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