A Game Theoretic Framework
for Power Control in Wireless
Sensor Networks
Shamik Sengupta, Mainak Chatterjee, and
Kevin A. Kwiat
IEEE TRANSACTIONS ON COMPUTERS,
2010
Outline
Introduction
Interference
Game
Nash Equilibrium
Numerical results
Conclusions
Comments
2
Introduction
Transmission at the optimal transmit power
level
High power level
High success probability
Energy is depleted faster
Increase the interference

“cascade” effect
3
Game theory have been used for solving
resource management problems
Network bandwidth allocation
Distributed database query optimization
Allocating resources in distributed systems such
as clusters, grids, and peer

to

peer networks
Achieve efficient energy usage through
optimal selection of the transmit power level
4
Interference
Randomly distributed nodes
Not contention

based protocol
But use code division multiplexing
Nonzero cross

correlation
The number of simultaneously active nodes
in the vicinity of a receiver is limited
5
Interference
Interference at node
w
from a local neighbor
node
u
.
6
Interference area is
Poisson distribution with node density as
The maximum number of interferers is
7
Game
Incomplete noncooperative game
Transmit at higher power will lead to a
noncooperative situation
Devise an equilibrium game strategy to
impose constraints on the nodes
strategy profile
space of strategy profiles
8
utility of node
i
is
utility vector
a node’s available information
its own power level
channel condition
expected SINR of neighboring receiver nodes
9
utility (node
i
transmit to node
j
)
efficiency function
P
e
: bit error rate (BER).
for example,
noncoherent FSK,
DPSK,
γ
j
:
the expected SINR of node
j
10
Nash Equilibrium
Net utility
cost function is a convex function of
s
i
.
Transmitting probability
is the probability density function of
s
i
11
The probability that any
l
nodes out of
N
nodes are active is given by
The expected net utility of
i
th node (if the
node is transmitting) is given by
12
Achievable gain (net utility considering both
modes: transmitting with
0 <
s
i
<
P
t
, and not
transmitting) obtained by node
i
is
Nash equilibrium point, the expected net
utility for transmitting and for being silent
should be equal at the threshold, i.e.,
s
i
=
P
t
.
13
Assume
T
1
be the solution
Suppose that a node unilaterally changes its
strategy and changes the threshold value to
T
2
Find that
14
Numerical results
15
16
17
DPSK
18
noncoherent PSK
19
20
21
22
23
Conclusions
Game

theoretic approach
Power control problem encountered in sensor
networks
Noncooperative games with incomplete
information
Existence of Nash equilibrium
if assume a minimum and maximum threshold for
channel condition and power level
24
Comments
Without simulation
Without comparison with other approach
How to know
γ
j
?
How to find out the transmit power thresholds
Optimal power control
25
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