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© 2007 Levente Buttyán and Jean-Pierre Hubaux
Security and Cooperation in Wireless Networks
http://secowinet.epfl.ch/
Chapter 11: Wireless operators in shared spectrum
multi-domain sensor networks;border games in cellular networks;
2/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Chapter outline
11.1 Multi-domain sensor networks11.2 Border games in cellular networks
3/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Typical cooperation: help in packet forwarding Can cooperation emerge spontaneously in multi-
domain sensor networks based solely on the self-interest of the sensor operators?
Multi-domain sensor networks
11.1 Multi-domain sensor networks
4/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Simplified model
C: Cooperation D: Defection
4 possible moves: CC – the sensor asks for help (cost 1) and helps if asked (cost 1) CD – the sensor asks for help (cost 1) and does not help (cost 0) DC – the sensor sends directly (cost 2) and helps if asked (cost 1) DD – the sensor sends directly (cost 2) and does not help (cost 0)
2α
11
1 1 1
11.1 Multi-domain sensor networks11.1.1 Simplified model
5/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Example : CC – CD (1/6)
CC – the sensor tries to get help from the other sensor and helps if the other sensor requests it
CD – the sensor tries to get help but it refuses to help
CC CD
11.1 Multi-domain sensor networks11.1.1 Simplified model
6/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Example : CC – CD (2/6)
CC – the sensor tries to get help from the other sensor and helps if the other sensor requests it
CD – the sensor tries to get help but it refuses to help
CC CD
11.1 Multi-domain sensor networks11.1.1 Simplified model
7/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Example : CC – CD (3/6)
CCfailure
CD
CC – the sensor tries to get help from the other sensor and helps if the other sensor requests it
CD – the sensor tries to get help but it refuses to help
11.1 Multi-domain sensor networks11.1.1 Simplified model
8/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Example : CC – CD (4/6)
CC CD
CC – the sensor tries to get help from the other sensor and helps if the other sensor requests it
CD – the sensor tries to get help but it refuses to help
11.1 Multi-domain sensor networks11.1.1 Simplified model
9/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Example : CC – CD (5/6)
CC CDsuccess
11.1 Multi-domain sensor networks11.1.1 Simplified model
10/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Example : CC – CD (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
11/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
2α
11
Cost for black Cost 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
12/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Reception threshold
time
success / failure of packet reception
Sliding window of history
Success(= 1)
Failure(= 0)
Receptionthreshold ρ
Average of the packet reception
Risk of going below threshold adapt strategy (move to theconstrained state: only DC or DDare 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
13/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
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
possible history 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
14/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Two-step Strategies
B – initial battery
ρ – reception threshold
– path loss exponent (2)
ε1,2 – payoff of transient states
Cooperative Nash equilibrium
Non-cooperative Nash equilibrium
If ρ > 1/3, then (CC/DD, CC/DD) is more desirable
11.1 Multi-domain sensor networks11.1.1 Simplified model
15/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
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)
16/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Main simulation parameters
Parameter Value
Number of sensors per domain 20
Area size 100 x 100 m
Reception threshold ρ 0.6
History length 5
Path loss exponent 2–3–4 (3)
11.1 Multi-domain sensor networks11.1.2 Generalized model
17/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Impact of the path loss exponentPerc
enta
ge o
f si
mula
tion
s
Equilibrium classes ( 0 – no cooperation, 1 – semi cooperation, 2 – full cooperation)
Value of the path loss exponent
– 2
– 3
– 4
11.1 Multi-domain sensor networks11.1.2 Generalized model
18/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Conclusion on multi-domain sensor networks
We examined whether cooperation is possible without the usage of incentives in multi-domain sensor networks
In the simplified model, the best Nash equilibria consist of cooperative strategies
In the generalized model, the best Nash equilibria belong to the cooperative classes in most of the cases
11.1 Multi-domain sensor networks
19/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Chapter outline
11.1 Multi-domain sensor networks11.2 Border games in cellular networks
20/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Motivating example
11.2 Border games in cellular networks
21/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Introduction
spectrum licenses do not regulate access over national borders
adjust pilot power to attract more users
Is there an incentive for operators to apply competitive pilot power control?
11.2 Border games in cellular networks
22/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
System model (1/2)
Network: cellular networks using CDMA
– channels defined by orthogonal codes
two operators: A and B one base station each pilot signal power 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
23/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
System model (2/2)
0
pilotp i ivpilot
iv pilot pilotown other
G P gSINR
N I I
W
i
pilotown iv iw
w
I g T
M
i
pilotother jv j iw
j i w
I g P T
M
A Bv
PAPB
TAv
TBw
TAw
0
trp iv ivtr
iv tr trown other
G T gSINR
N I I
W
, i
pilotown iv i iw
w v w
I g P T
M
tr pilotother otherI I
pilot signal SINR:
traffic signal SINR:
Pi – pilot power of i
– processing gain for the pilot signalpilotpG
ivg
0N – noise energy per symbol
W
ivT
pilotownI
– channel gain between BS i and user v
– available bandwidth
– own-cell interference affecting the pilot signal
– own-cell interference factor
– traffic power between BS i and 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
24/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
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 vv
u
M
v
max , ,
,i
S S Si i i
si S S
i
u s P u P P
u P P
11.2 Border games in cellular networks11.2.2 Power control game
25/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Simulation settings
11.2 Border games in cellular networks11.2.2 Power control game
26/33Security and Cooperation in Wireless NetworksChapter 11: Wireless operators in shared spectrum
Is there a game?
only A is strategic (B uses PB = PS) 10 data users path loss exponent, α = 2
Δi
11.2 Border games in cellular networks11.2.2 Power control game
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When both operators are strategic
10 data users path loss exponent, α = 4
11.2 Border games in cellular networks11.2.2 Power control game
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Nash equilibria
10 data users 100 data users
11.2 Border games in cellular networks11.2.2 Power control game
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Efficiency (1/2)
10 data users
11.2 Border games in cellular networks11.2.2 Power control game
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Efficiency (2/2)
100 data users
11.2 Border games in cellular networks11.2.2 Power control game
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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
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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
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Conclusion on border games
not only individual nodes may exhibit selfish behavior, but operators can be selfish too
example: adjusting pilot power to attract more users at national borders
the problem can be modeled as a game between the operators– the game has an efficient Nash equilibrium– there’s a simple convergence algorithm that drives the
system into the Nash equilibrium
11.2 Border games in cellular networks