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 relation over
the set of action profiles.
Or
For each play
(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 the integral
(b)
Use integration by parts to show that
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 8
10.
x+2
dx
2
x + 2x 8
0
7.
sin xe
9.
x +1
dx
2
2
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.
(rx-5f(rx-t3)
4
g.nx- cDsL
ta)srnr]
c'sx - 3C"'
[^tng)
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 functions, find and classify the stationary points and h
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 -,)2- 4
q.
9'r')
b.
3
"'4 5 , Ll
5" t-+, ,6rJ
-? s y <l L
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 TWO Hours
Candidates may complete the front cover of t
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 player can now condition his action on previous
actions
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 output is Q then market price is
P(Q), where P is nonincreas
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 moves first choosing C or D. Then players II
and III m
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
or not. If it enters, the incumbent may either
accommoda
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
Preferences
Complete
Consistent (transitive)
Rational
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 TWO Hours
Candidates may complete the front cover of t
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 of stress and strain
!Calculating the oscillations of a
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)
If the domain of this function is cfw_x : -1 x < 2, w
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
University of Nottingham
MM1SM1 Mechanics of Solids 1
University of Nottingham
S1.0 : Shear