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2007 Levente Buttyn and Jean-Pierre Hubaux
Security and Cooperationin Wireless Networks
http://secowinet.epfl.ch/
Chapter 11: Wireless operators in sharedspectrum
multi-domain sensornetworks;
border games incellular networks;
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Chapter outline
11.1 Multi-domain sensor networks
11.2 Border games in cellular networks
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Typical cooperation: help in packet forwarding
Can cooperation emerge spontaneously in multi-domainsensor networks based solely on the self-interest of thesensor operators?
Multi-domain sensor networks
11.1 Multi-domain sensor networks
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Simplified model
C: Cooperation D: Defection
4 possible moves:
CCthe sensor asks for help (cost 1) and helps if asked (cost 1) CDthe sensor asks for help (cost 1) and does not help (cost 0)
DCthe sensor sends directly (cost 2a) and helps if asked (cost 1)
DDthe sensor sends directly (cost 2a) and does not help (cost 0)
2
11
1 1 1
11.1 Multi-domain sensor networks11.1.1 Simplified model
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Example : CCCD (1/6)
CCthe sensor tries to get help from the other sensorand helps if the other sensor requests it
CDthe sensor tries to get help but it refuses to help
CC CD
11.1 Multi-domain sensor networks11.1.1 Simplified model
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Example : CCCD (2/6)
CCthe sensor tries to get help from the other sensorand helps if the other sensor requests it
CDthe sensor tries to get help but it refuses to help
CC CD
11.1 Multi-domain sensor networks11.1.1 Simplified model
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Example : CCCD (3/6)
CC
failure
CD
CCthe sensor tries to get help from the other sensorand helps if the other sensor requests it
CDthe sensor tries to get help but it refuses to help
11.1 Multi-domain sensor networks11.1.1 Simplified model
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Example : CCCD (4/6)
CC CD
CCthe sensor tries to get help from the other sensorand helps if the other sensor requests it
CDthe sensor tries to get help but it refuses to help
11.1 Multi-domain sensor networks11.1.1 Simplified model
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Example : CCCD (5/6)
CC CDsuccess
11.1 Multi-domain sensor networks11.1.1 Simplified model
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Example : CCCD (6/6)
CC CD
Black player
Cost: 2
1 for asking
1 for helping
Benefit: 0
(packet dropped)
Gray player
Cost: 1
1 for asking
Benefit: 1
(packet arrived)
11.1 Multi-domain sensor networks11.1.1 Simplified model
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2
11
Cost for blackCost for grey
Outcome for black (0 = failure)
Outcome for grey (1 = success)
The simplified model in strategic form
11.1 Multi-domain sensor networks11.1.1 Simplified model
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Reception threshold
time
success / failure of packet reception
Sliding window of history
Success
(= 1)
Failure
(= 0)
Reception
threshold
Average of the packet reception
Risk of going below threshold
adapt strategy (move to theconstrained state: only DC or DD
are eligible)
Reception threshold: computed and stored at each sensor node
The battery (B) level of the sensors decreases with the moves
If the battery is empty, the sensor dies
11.1 Multi-domain sensor networks11.1.1 Simplified model
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Game Theoretic Approach
The mentioned concepts describe a game
Players: network operators
Moves (unconstrained state): CC, CD, DC, DD
Moves (constrained state): DC, DD
Information sets: histories
Strategy: function that assigns a move to every possiblehistory considering the weight threshold
Payoff = lifetime
We are searching for Nash equilibria with the highest
lifetimes
11.1 Multi-domain sensor networks11.1.1 Simplified model
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Two-step Strategies
Binitial battery
reception threshold
apath loss exponent (2)
1,2payoff of transient states
Cooperative Nash equilibrium
Non-cooperative Nash equilibrium
If > 1/3, then (CC/DD, CC/DD) is more desirable
11.1 Multi-domain sensor networks11.1.1 Simplified model
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Generalized Model
11.1 Multi-domain sensor networks11.1.2 Generalized model
Simplified model with the following extensions: many sensors, random placing
minimum energy path routing common sink / separate sink scenarios
classification of equilibria Class 0: no cooperation (no packet is relayed)
Class 1: semi cooperation (some packets are relayed)
Class 2: full cooperation (all packets are relayed)
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Main simulation parameters
Parameter Value
Number of sensors per domain 20
Area size 100 x 100 m
Reception threshold 0.6
History length 5
Path loss exponent 234 (3)
11.1 Multi-domain sensor networks11.1.2 Generalized model
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Impact of the path loss exponent
Percentageofs
imulations
Equilibrium classes ( 0no cooperation, 1semicooperation, 2full cooperation)
Value of the pathloss exponent
2
3
4
11.1 Multi-domain sensor networks11.1.2 Generalized model
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Conclusion on multi-domain sensor networks
We examined whether cooperation is possible without theusage of incentives in multi-domain sensor networks
In the simplified model, the best Nash equilibria consist ofcooperative strategies
In the generalized model, the best Nash equilibria belong tothe cooperative classes in most of the cases
11.1 Multi-domain sensor networks
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Chapter outline
11.1 Multi-domain sensor networks
11.2 Border games in cellular networks
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Motivating example
11.2 Border games in cellular networks
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Introduction
spectrum licenses do notregulate access overnational borders
adjust pilot power toattract more users
Is there an incentive for operators to apply competitive
pilot power control?
11.2 Border games in cellular networks
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System model (1/2)
Network:
cellular networks using CDMA channels defined by orthogonal
codes
two operators: A and B
one base station each
pilot signalpower control
Users:
roaming users
users uniformly distributed
select the best quality BS
selection based signal-to-interference-plus-noise ratio(SINR)
11.2 Border games in cellular networks11.2.1 Model
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System model (2/2)
0
pilot
p i ivpilotiv pilot pilot
own other
G P gSINRN I I
W
i
pilot
own iv iw
w
I g T
M
i
pilot
other jv j iw
j i w
I g P T
M
A Bv
PA
PB
TAv
TBw
TAw
0
tr
p iv ivtr
iv tr tr
own other
G T gSINR
N I I
W
, i
pilot
own iv i iw
w v w
I g P T
M
tr pilot
other other I I
pilot signal SINR:
traffic signal SINR:
Pi
pilot power of i
processing gain for the pilot signal
pilot
pG
ivg
0N noise energy per symbol
W
ivT
pilot
ownI
channel gain between BS iand user v
available bandwidth
own-cell interference affecting the pilot signal
own-cell interference factor
traffic power between BS iand user v
other-to-own-cell interference factor
iM set of users attached to BS i
11.2 Border games in cellular networks11.2.1 Model
h d l
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Game-theoretic model
Power Control Game, GPC players networks operators (BSs), A and B strategy pilot signal power, 0W < Pi < 10W, i= {A, B}
standard power, PS= 2W
payoff profit, where is the expected income
serving user v normalized payoff difference:
i
i v
v
u
M
v
max , ,
,
i
S S S
i i is
iS S
i
u s P u P P
u P P
11.2 Border games in cellular networks11.2.2 Power control game
Si l i i
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Simulation settings
11.2 Border games in cellular networks11.2.2 Power control game
I th ?
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Is there a game?
only A is strategic (B uses PB= PS)
10 data users
path loss exponent, = 2
i
11.2 Border games in cellular networks11.2.2 Power control game
Wh b th t t t i
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When both operators are strategic
10 data users
path loss exponent, = 4
11.2 Border games in cellular networks11.2.2 Power control game
N h ilib i
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Nash equilibria
10 data users 100 data users
11.2 Border games in cellular networks11.2.2 Power control game
Effi i (1/2)
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Efficiency (1/2)
10 data users
11.2 Border games in cellular networks11.2.2 Power control game
Effi i (2/2)
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Efficiency (2/2)
100 data users
11.2 Border games in cellular networks11.2.2 Power control game
C t NE (1/2)
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convergence based on better-response dynamics
convergence step: 2 W
Convergence to NE (1/2)
PA= 6.5 W
11.2 Border games in cellular networks11.2.3 Convergence to a Nash Equilibrium
Con e gence to NE (2/2)
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Convergence to NE (2/2)
convergence step: 0.1 W
11.2 Border games in cellular networks11.2.3 Convergence to a Nash Equilibrium
Conclusion on border games
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Security and Cooperation in Wireless Networks
Conclusion on border games
not only individual nodes may exhibit selfish behavior, butoperators can be selfish too
example: adjusting pilot power to attract more users atnational borders
the problem can be modeled as a game between theoperators
the game has an efficient Nash equilibrium
theres a simple convergence algorithm that drives the system intothe Nash equilibrium