Non-Cooperative Behavior
in Wireless Networks
Márk Félegyházi (EPFL)
PhD. defense – April 2007
Prospective wireless networks
Relaxing spectrum licensing:
►
small network operators in unlicensed bands
–
–
►
community and ad hoc networks
–
–
►
no authority
peer-to-peer network operation
cognitive radio
–
–
–
April 2007
inexpensive access points
flexible deployment
restricted operation in any frequency band
no interference with licensed (primary) users
adaptive behavior
Márk Félegyházi (EPFL) - PhD defense
2
Motivation
TRENDS
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OUTCOME
►
►
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more complexity at the network edges
decentralization
ease of programming for wireless devices
rational users

more adaptive wireless devices
potential selfish behavior of devices
What is the effect of selfish behavior in wireless networks?
April 2007
Márk Félegyházi (EPFL) - PhD defense
3
Game theory in networking
►
Peer-to-peer networks
–
–
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Wired networks
–
–
–
►
free-riding [Golle et al. 2001, Feldman et al. 2007]
trust modeling [Aberer et al. 2006]
congestion pricing [Korilis et al. 1995, Korilis and Orda 1999, Johari and
Tsitsiklis 2004]
bandwidth allocation [Yaïche et al. 2000]
coexistence of service providers [Shakkottai and Srikant 2005/2006, He
and Walrand 2006]
Wireless networks
–
–
–
–
April 2007
power control [Goodman and Mandayam 2001, Alpcan et al. 2002, Xiao
et al. 2003]
resource/bandwidth allocation [Marbach and Berry 2002, Qui and
Marbach 2003]
medium access [MacKenzie and Wicker 2003, Yuen and Marbach 2005,
Čagalj et al. 2005]
Wi-Fi pricing [Musacchio and Walrand 2004/2006]
Márk Félegyházi (EPFL) - PhD defense
4
Outline of the thesis
Part I:
Introduction to game theory
►
►
Part II:
Non-cooperative users
►
►
Part III:
Non-cooperative network
operators
April 2007
►
►
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Ch 1: A tutorial on game theory
Ch. 2: Multi-radio channel allocation in wireless networks
Ch. 3: Packet forwarding in static ad-hoc networks
Ch. 4: Packet forwarding in dynamic ad-hoc networks
Ch. 5: Packet forwarding in multi-domain sensor networks
Ch. 6: Cellular operators in a shared spectrum
Ch. 7: Border games in cellular networks
Márk Félegyházi (EPFL) - PhD defense
5
Part II: Non-Cooperative Users
Chapter 2:
Multi-Radio Channel Allocation in
Wireless Networks
Related Work
►
Channel allocation
–
–
–
►
Multi-radio networks
–
–
►
in cellular networks: fixed and dynamic: [Katzela and Naghshineh 1996,
Rappaport 2002]
in WLANs [Mishra et al. 2005]
in cognitive radio networks [Zheng and Cao 2005]
mesh networks [Adya et al. 2004, Alicherry et al. 2005]
cognitive radio [So et al. 2005]
Competitive medium access
–
–
–
–
April 2007
Aloha [MacKenzie and Wicker 2003, Yuen and Marbach 2005]
CSMA/CA [Konorski 2002, Čagalj et al. 2005]
WLAN channel coloring [Halldórsson et al. 2004]
channel allocation in cognitive radio networks [Cao and Zheng 2005, Nie
and Comaniciu 2005]
Márk Félegyházi (EPFL) - PhD defense
7
Problem
d2
d1
►
►
multi-radio devices
set of available channels
d5
d4
d3
d6
How to assign radios to available channels?
April 2007
Márk Félegyházi (EPFL) - PhD defense
8
System model (1/3)
►
►
►
►
►
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C – set of orthogonal
channels (|C| = C)
N – set of communicating
pairs of devices (|N| = N)
sender and receiver are
synchronized
single collision domain if
they use the same channel
devices have multiple radios
k radios at each device, k ≤ C
April 2007
p1
d2
d1
d5
d4
d3
Márk Félegyházi (EPFL) - PhD defense
p2
p3
d6
9
System model (2/3)
►
►
channels with the same properties
τ() – total throughput on any channel x
1
number of links
April 2007
Márk Félegyházi (EPFL) - PhD defense
10
System model (3/3)
►
►
►
N communicating pairs of devices
C orthogonal channels
k radios at each device (k links for
each pair)
ki , x→
number of links by
pair i on channel x
ki   ki , x
xC
k x   ki , x
example:
Intuition: ki , x  1
multiple communication links
on one channel ?
April 2007
Márk Félegyházi (EPFL) - PhD defense
iN
kc2  3
k p3  4
k p3 ,c2  2
11
Multi-radio channel allocation (CA) game
►
►
selfish users (communicating pairs)
non-cooperative game GCA
– players → communicating pairs
– strategy → channel allocation
– payoff → total throughput
si  ki ,1 ,..., ki ,C 
►
strategy:
►
strategy matrix:
►
payoff:
 s1 
 
S    
s 
 N
 ki , x

ui   i   
 ( k x ) 
xC  k x

April 2007
Márk Félegyházi (EPFL) - PhD defense
12
Use of all radios
Lemma: If S* is a NE in GCA, then ki  k , i.
Each player should use all of his radios.
Intuition: Player i is always better of deploying unused radios.
p4 p4
Lemma
all channel allocations
April 2007
Márk Félegyházi (EPFL) - PhD defense
13
Load-balancing channel allocation
►
►
Consider two arbitrary
channels x and y, where
ky ≥ kx
distance: dy,x = ky – kx
Proposition: If S* is a NE in GCA, then dy,x ≤ 1, for any
channel x and y.
NE candidate:
Proposition
Lemma
all channel allocations
April 2007
Márk Félegyházi (EPFL) - PhD defense
14
Nash equilibria (1/2)
►
►
Consider two arbitrary
channels x and y, where
ky ≥ kx
distance: dy,x = ky – kx
p4
p2
Theorem (case 1): If for any two channels x and y in C it is true that
ki,x ≤ 1, for all i and dy,x ≤ 1, then S* is a Nash equilibrium.
Nash
Equilibrium:
Use one link per channel.
Proposition
Lemma
all channel allocations
NE case 1
April 2007
Márk Félegyházi (EPFL) - PhD defense
15
Nash equilibria (2/2)
►
Consider two arbitrary
d = ky – kx
channels x and y, where y,x
di,y,x = ki,y – ki,x
ky ≥ kx
Cmax
→
Cmin
channels with the
minimum/maximum
number of links
Theorem (case 2): If dy,x ≤ 1 for x,y in C and there exists j in N and x’
in Cmin such that kj,x’ > 1, in addition kj,y’ ≤ 1 for all y’ in Cmax and
di,x’,x’’ ≤ 1 for any x’,x’’ in Cmin, then S* is a Nash equilibrium.
Nash
Equilibrium:
Use multiple links
on certain channels.
Proposition
Lemma
all channel allocations
NE case 1
April 2007NE case 2
Márk Félegyházi (EPFL) - PhD defense
16
Efficiency (1/2)
Theorem: In GCA, the price of anarchy is:
POA 
 1
N k 

 kx  1 
    k x     k x  1     k x  1
C 

 N k 
 N k 
, kx  1  
where k x  


C
C




Corollary: If the throughput function τ() is constant (ex.
theoretical CSMA/CA), then any Nash equilibrium
channel allocation is Pareto-optimal in GCA.
April 2007
Márk Félegyházi (EPFL) - PhD defense
17
Efficiency (2/2)
►
►
►
CSMA/CA protocol
In theory, the throughput function τ() is constant  POA = 1
In practice, there are collisions, but τ() decreases slowly with kx (due to the
RTS/CTS method)
G. Bianchi, “Performance Analysis of the IEEE 802.11 Distributed Coordination Function,”
in IEEE Journal on Selected Areas of Communication (JSAC), 18:3, Mar. 2000
April 2007
Márk Félegyházi (EPFL) - PhD defense
18
Convergence to NE (1/3)
Algorithm with imperfect info:
► move links from “crowded”
channels to other randomly
chosen channels
► desynchronize the changes
► convergence is not ensured
p5
p3
p2
p1
April 2007
p5: c2→c5
c6→c4
p3: c2→c5
c6→c4
c1→c3
p2: c2→c5
p1: c2→c5
c6→c4
p1
p4
N = 5, C = 6, k = 3
p
5
p1: c4→c6
c5→c2
p4: idle
time
p
p
p
4
5
p
4
p
3
p
3
p
2
p
p
5
p
3
1
1
2
2
c6 channels
p
p
4
p
c1 c2 c3 c4 c5
Márk Félegyházi (EPFL) - PhD defense
p
1
19
Convergence to NE (2/3)
Algorithm with imperfect info:
► move links from “crowded”
channels to other randomly
chosen channels
► desynchronize the changes
► convergence is not ensured
 S   7
15  7 3
 S  

15  3 4
Balance:   S    k x 
xC
N k
C
best balance (NE):
unbalanced (UB):
 UB   3
 UB   15
Efficiency:   S  
 ( SUB )   ( S )
 ( SUB )   ( S NE )
0   S  1
April 2007
Márk Félegyházi (EPFL) - PhD defense
20
Convergence to NE (3/3)
N (# of pairs)
10
C (# of channels)
8
k (radios per device)
3
τ(1) (max. throughput) 54 Mbps
April 2007
Márk Félegyházi (EPFL) - PhD defense
21
Summary – Non-cooperative users
►
►
►
►
wireless networks with multi-radio devices
users of the devices are selfish players
GCA – channel allocation game
results for a Nash equilibrium:
–
–
–
–
►
►
►
fairness issues
coalition-proof equilibria
algorithms to achieve efficient NE:
–
–
April 2007
players should use all their radios
load-balancing channel allocation
two cases of Nash equilibria
NE are efficient both in theory and practice
centralized algorithm with perfect information
distributed algorithm with imperfect information
Márk Félegyházi (EPFL) - PhD defense
22
Part III: Non-Cooperative
Network Operators
Chapter 7:
Border Games in Cellular Networks
Related Work
►
Power control in cellular networks
–
–
–
►
Coexistence of service providers
–
–
April 2007
up/downlink power control in CDMA [Hanly and Tse 1999,
Baccelli et al. 2003, Catrein et al. 2004]
pilot power control in CDMA [Kim et al. 1999, Värbrand and
Yuan 2003]
using game theory [Alpcan et al. 2002, Goodman and
Mandayam 2001, Ji and Huang 1998, Meshkati et al. 2005, Lee
et al. 2002]
wired [Shakkottai and Srikant 2005, He and Walrand 2006]
wireless [Shakkottai et al. 2006, Zemlianov and de Veciana
2005]
Márk Félegyházi (EPFL) - PhD defense
24
Problem
►
►
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?
April 2007
Márk Félegyházi (EPFL) - PhD defense
25
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-tointerference-plus-noise ratio
(SINR)
►
April 2007
Márk Félegyházi (EPFL) - PhD defense
26
System model (2/2)
pilot signal SINR:
SINRivpilot 
pilot
I own
TAw
G ppilot  Pi  giv
N0  W  I
pilot
own
I
I


   giv   Pi   Tiw 
w  v , wM i


tr
pilot
I other
 I other
April 2007
PB
PA


   giv    Tiw 
 wM i 


I
    g jv   Pj   Tiw 
j i
wM i


traffic signal SINR:
tr
G
p  Tiv  g iv
tr
SINRiv 
tr
tr
N 0  W  I own
 I other
pilot
own
TAv
pilot
other
pilot
other
TBw
A
Pi
v
B
– pilot power of i
Gppilot – processing gain for the pilot signal
giv – channel gain between BS i and user v
N0
W
– noise energy per symbol
– available bandwidth
pilot
– own-cell interference affecting the pilot signal
I own

Tiv
– own-cell interference factor
– traffic power between BS i and user v
Mi
– set of users attached to BS i

– other-to-own-cell interference factor
Márk Félegyházi (EPFL) - PhD defense
27
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, ui   v where v is the expected income
vM i
serving user v
– normalized payoff difference:
–
i 
April 2007

max ui  si , P S   ui  P S , P S 
si
ui  P S , P S 
Márk Félegyházi (EPFL) - PhD defense

28
Simulation
April 2007
Márk Félegyházi (EPFL) - PhD defense
29
Is there a game?
►
►
►
only A is strategic (B uses PB = PS)
10 data users
path loss exponent, α = 2
Δi
April 2007
Márk Félegyházi (EPFL) - PhD defense
30
Strategic advantage
►
normalized payoff difference:
i 
April 2007

max ui  si , P S   ui  P S , P S 
si
ui  P S , P S 
Márk Félegyházi (EPFL) - PhD defense

31
Payoff of A
►
►
April 2007
Both operators are strategic
path loss exponent, α = 4
Márk Félegyházi (EPFL) - PhD defense
32
Nash equilibrium
►
►
unique NE
NE power P* is higher than PS
April 2007
Márk Félegyházi (EPFL) - PhD defense
33
Efficiency
►
April 2007
10 data users
zero-sum game
Márk Félegyházi (EPFL) - PhD defense
34
Convergence to NE (1/2)
►
►
convergence based on better-response dynamics
convergence step: 2 W
PA = 6.5 W
April 2007
Márk Félegyházi (EPFL) - PhD defense
35
Convergence to NE (2/2)
►
convergence step: 0.1 W
April 2007
Márk Félegyházi (EPFL) - PhD defense
36
Summary – Non-cooperative network operators
►
►
►
►
►
two operators on a national border
single-cell model
pilot power control
roaming users
power control game, GPC
–
–
►
►
operators have an incentive to be strategic
NE are efficient, but they use high power
simple convergence algorithm
extended game with power cost
–
April 2007
Prisoner’s Dilemma
Márk Félegyházi (EPFL) - PhD defense
37
Summary
Thesis contributions
(Ch. 1: A tutorial on game theory)
►
facilitate the application of game theory in wireless networks
M. Félegyházi and J.-P. Hubaux, “Game Theory in Wireless Networks: A Tutorial,” submitted to ACM Communication
Surveys, 2006
April 2007
Márk Félegyházi (EPFL) - PhD defense
39
Thesis contributions
(Ch. 2: Multi-radio channel allocation in wireless networks)
►
►
NE are efficient and sometimes fair, and they can be reached
even if imperfect information is available
–
each player has one radio per
channel
– some players have multiple radios
on certain channels
►
►
►
►
p1
load-balancing Nash equilibria
NE are Pareto-efficient both in
theory and practice
fairness issues
coalition-proof equilibria
convergence algorithms to
efficient NE
d2
d1
d5
d4
d3
p2
p3
d6
M. Félegyházi, M. Čagalj, S. S. Bidokhti, and J.-P. Hubaux, “Non-cooperative Multi-radio Channel Allocation in Wireless
Networks,” in Proceedings of Infocom 2007, Anchorage, USA, May 6-12, 2007
April 2007
Márk Félegyházi (EPFL) - PhD defense
40
Thesis contributions
(Ch. 3: Packet forwarding in static ad-hoc networks)
►
incentives are needed to promote cooperation in ad hoc networks
►
model and meta-model using
game theory
dependencies / dependency graph
study of NE
►
►
–
in theory, NE based on
cooperation exist
– in practice, the necessary
conditions for cooperation do not
hold
►
part of the network can still
cooperate
M. Félegyházi, L. Buttyán and J.-P. Hubaux, “Nash Equilibria of Packet Forwarding Strategies in Wireless Ad Hoc
Networks,” in Transactions on Mobile Computing (TMC), vol. 5, nr. 5, May 2006
April 2007
Márk Félegyházi (EPFL) - PhD defense
41
Thesis contributions
(Ch. 4: Packet forwarding in dynamic ad-hoc networks)
►
►
►
►
►
mobility helps cooperation in ad hoc networks
spontaneous cooperation exists on
a ring (theoretical)
cooperation resistant to drift
(alternative cooperative strategies)
to some extent
in reality, generosity is needed
as mobility increases, less
generosity is needed
M. Félegyházi, L. Buttyán and J.-P. Hubaux, “Equilibrium Analysis of Packet Forwarding Strategies in Wireless Ad Hoc
Networks - the Dynamic Case,” Technical report - LCA-REPORT-2003-010, 2003
April 2007
Márk Félegyházi (EPFL) - PhD defense
42
Thesis contributions
(Ch. 5: Packet forwarding in multi-domain sensor networks)
►
►
►
►
sharing sinks is beneficial and sharing sensors is also in
certain scenarios
energy saving gives a natural
incentive for cooperation
sharing sinks
with common sinks, sharing
sensors is beneficial
–
in sparse networks
– in hostile environments
M. Félegyházi, L. Buttyán and J.-P. Hubaux, “Cooperative Packet Forwarding in Multi-Domain Sensor Networks,” in
PerSens 2005, Kauai, USA, March 8, 2005
April 2007
Márk Félegyházi (EPFL) - PhD defense
43
Thesis contributions
(Ch. 6: Cellular operators in a shared spectrum)
both cooperation (low powers) and defection (high powers)
exist, but cooperation can be enforced by punishments
►
►
►
wireless operators compete in a
shared spectrum
single stage game
–
►
repeated game
–
►
various Nash equilibria in the grid
scenario, depending on
cooperation parameters
RMIN (cooperation) is enforceable
with punishments
general scenario = arbitrary ranges
–
the problem is NP-complete
M. Félegyházi and J.-P. Hubaux, “Wireless Operators in a Shared Spectrum,” in Proceedings of Infocom 2006, Barcelona,
Spain, April 23-29, 2006
April 2007
Márk Félegyházi (EPFL) - PhD defense
44
Thesis contributions
(Ch. 7: Border games in cellular networks)
►
►
►
operators have an incentive to adjust their pilot power on
the borders
competitive power control on a
national border
power control game
–
operators have an incentive to be
strategic
– NE are efficient, but they use high
power
►
►
simple convergence algorithm
extended game corresponds to the
Prisoner’s Dilemma
M. Félegyházi, M. Čagalj, D. Dufour, and J.-P. Hubaux, “Border Games in Cellular Networks,” in Proceedings of Infocom
2007, Anchorage, USA, May 6-12, 2007
April 2007
Márk Félegyházi (EPFL) - PhD defense
45
Selected publications
(à la Prof. Gallager)
►
►
►
April 2007
M. Félegyházi, M. Čagalj, S. S. Bidokhti, and J.-P. Hubaux, “NonCooperative Multi-Radio Channel Allocation in Wireless Networks,” in
Infocom 2007
M. Félegyházi, M. Čagalj, D. Dufour, and J.-P. Hubaux, “Border Games in
Cellular Networks,” in Infocom 2007
M. Félegyházi, L. Buttyán and J.-P. Hubaux, “Nash Equilibria of Packet
Forwarding Strategies in Wireless Ad Hoc Networks,” in IEEE Transactions
on Mobile Computing (TMC), vol. 5, nr. 5, 2006
Márk Félegyházi (EPFL) - PhD defense
46
Future research directions (1/3)
►
Cognitive networks
–
–
–
Chapter 2: multi-radio channel allocation
adaptation is a fundamental property of cognitive devices
selfishness is threatening network performance
• primary (licensed) users
• secondary (cognitive) users
–
incentives are needed to prevent selfishness
• frequency allocation
• interference control
submitted: M. Félegyházi, M. Čagalj and J.-P. Hubaux, “Efficient MAC in Cognitive Radio Systems: A Game-Theoretic
Approach,” submitted to IEEE JSAC, Special Issue on Cognitive Radios, 2008
April 2007
Márk Félegyházi (EPFL) - PhD defense
47
Future research directions (2/3)
►
Coexistence of wireless networks
–
–
–
Chapter 6 and 7: wireless operators in shared spectrum
advancement of wireless technologies
alternative service providers
• small operators
• social community networks
–
–
competition becomes more significant
coexistence results in nonzero-sum games
• mechanism to enforce cooperation
• competition improves services
in preparation: M. H. Manshaei, M. Félegyházi, J. Freudiger, J.-P. Hubaux, and P. Marbach, “Competition of Wireless
Network Operators and Social Networks,” to be submitted in 2007
April 2007
Márk Félegyházi (EPFL) - PhD defense
48
Future research directions (3/3)
►
Economics of security and privacy
–
cryptographic building blocks are quite reliable (some
people might disagree)
– implementation fails due to economic reasons (3C)
• confusion in defining security goals
• cost of implementation
• complexity of usage
–
–
privacy is often not among the security goals
incentives to implement correct security measures
• share liabilities
• better synchronization
• collaboration to prevent attacks
submitted: J. Freudiger, M. Raya, M. Félegyházi, and J.-P. Hubaux, “On Location Privacy in Vehicular Mix-Networks,”
submitted to Privacy Enhancing Technologies 2007
April 2007
Márk Félegyházi (EPFL) - PhD defense
49
Extensions
Introduction to Game Theory
Chapter 1:
A Tutorial on Game Theory
The Channel Allocation Game
►
two channels: c1 and c2
–
►
►
►
►
total available throughput:  c1  3 and  c2  2
two devices: p1 and p2
throughput is fairly shared
users of the devices are rational

c1
f1
c2
f2
f3
Channel Allocation (CA) Game: GCA = (N, S, U)
–
–
N – players: p1 and p2
S – strategies: choosing the channels
•
–
U – payoff functions: received throughputs
•
April 2007
s1  {c1 , c2 } and s2  {c1 , c2 }
u1   p1 and u2   p2
Márk Félegyházi (EPFL) - PhD defense
si  S strategy of player i
s  (s1 , s2 ) strategy profile
ui  U payoff of player i
52
Strategic form
►
the CA game in strategic form
p2
p1
April 2007
c1
c2
c1
1.5,1.5
3,2
c  3
c2
2,3
1,1
c  2
Márk Félegyházi (EPFL) - PhD defense
1
2
53
Stability: Nash Equilibrium
Best response: Best strategy of player i given the strategies of others.
bri ( si )  si  S : ui ( si , si )  ui ( si' , si ), si'  S 
Nash equilibrium: No player has an incentive to unilaterally deviate.
ui ( si* , s* i )  ui ( si , s* i ), si  S
p2
p1
April 2007
c1
c2
c1
1.5,1.5
3,2
c  3
c2
2,3
1,1
c  2
Márk Félegyházi (EPFL) - PhD defense
1
2
54
Efficiency: Pareto-Optimality
Pareto-optimality: The strategy profile spo is Pareto-optimal if:
s ' : ui ( s ' )  ui ( s po ), i with strict inequality for at least one player i
Price of anarchy: The ratio between the total payoff of players playing a
socially-optimal (max. Pareto-optimal) strategy and a worst Nash
equilibrium.
POA 
so
u
i
p2
i
w  NE
u
i
c1
c2
c1
1.5,1.5
3,2
c  3
c2
2,3
1,1
c  2
i
p1
April 2007
Márk Félegyházi (EPFL) - PhD defense
1
2
55
Fairness
Nash equilibria (case 1)
fair
Nash equilibria (case 2)
unfair
Theorem: A NE channel allocation S* is max-min fair iff
 ki, x   k j , x , i, j  N
xCmin
xCmin
Intuition: This implies equality: ui = uj, i,j  N
April 2007
Márk Félegyházi (EPFL) - PhD defense
56
Centralized algorithm
Assign links to the channels sequentially.
p
p
p
p
4
4
p
4
p
p
p
p
2
p
p
2
3
p
3
p
3
p
3
1
1
1
1
2
2
p
April 2007
4
p
Márk Félegyházi (EPFL) - PhD defense
57
System model UMTS
►
basic elements of DS-CDMA:
required
CIR
input
data
channel
encoder
modulator
PR pattern
generator
►
channel
required
SINR
demodulator
channel
decoder
output
data
PR pattern
generator
UMTS parameters:
D. Tse and P. Viswanath, “Fundamentals of Wireless Communication,” Cambride Univ. Press, 2005
H. Holma and A. Toskala, eds. “WCDMA for UMTS,” John Wiley & Sons, Inc., 2002
April 2007
Márk Félegyházi (EPFL) - PhD defense
58
Nash equilibrium (2/2)
April 2007
Márk Félegyházi (EPFL) - PhD defense
59
Efficiency (2/2)
Price of conformance: Ratio between the total payoff in a Paretooptimal strategy profile and the one using the standard power, PS
April 2007
Márk Félegyházi (EPFL) - PhD defense
60
Extended Game with Power Costs
►
►
►
M users in total
cost for high power C
payoff difference Δ
Prisoner’s Dilemma
► M = 10
► C = 1
► Δ= 2
p2
p2
PS
P*
PS
M/2, M/2
M/2-Δ,
M/2+Δ-C
P*
M/2+Δ-C,
M/2-Δ
M/2-C,
M/2-C
p1
April 2007
PS
P*
PS
5, 5
3, 6
P*
6, 3
4, 4
p1
Márk Félegyházi (EPFL) - PhD defense
61
Thesis contributions
►
Ch 1: A tutorial on game theory
–
►
Ch. 2: Multi-radio channel allocation in wireless networks
–
►
sharing sinks is beneficial and sharing sensors is also in certain scenarios
Ch. 6: Cellular operators in a shared spectrum
–
►
mobility helps cooperation in ad hoc networks
Ch. 5: Packet forwarding in multi-domain sensor networks
–
►
incentives are needed to promote cooperation in ad hoc networks
Ch. 4: Packet forwarding in dynamic ad-hoc networks
–
►
NE are efficient and sometimes fair, and the fair NE can be reached even
if imperfect information is available
Ch. 3: Packet forwarding in static ad-hoc networks
–
►
facilitate the application of game theory in wireless networks
both cooperation (low powers) and defection (high powers) exist, but
cooperation can be enforced by punishments
Ch. 7: Border games in cellular networks
–
April 2007
operators have an incentive to adjust their pilot power on the borders
Márk Félegyházi (EPFL) - PhD defense
62
Thesis contributions (1/3)
►
Ch 1: A tutorial on game theory
“facilitate the application of game theory in wireless networks”
– comprehensive introduction to game theory
– educational value – selected examples for wireless engineers
►
Ch. 2: Multi-radio channel allocation in wireless networks
“NE are efficient and sometimes fair, and the fair NE can be reached even if
imperfect information is available”
– game-theoretic model of competitive channel allocation of multi-radio
devices
– the existence of load-balancing Nash equilibria
• each player has one radio per channel
• some players have multiple radios on certain channels
–
–
NE are Pareto-efficient both in theory and practice
convergence algorithms to efficient NE
•
•
•
•
–
April 2007
centralized algorithm with perfect information
distributed algorithm with perfect information
distributed algorithm with imperfect information
proof of convergence for each algorithm
coalition-proof equilibria
Márk Félegyházi (EPFL) - PhD defense
63
Thesis contributions (2/3)
►
Ch. 3: Packet forwarding in static ad-hoc networks
“incentives are needed to promote cooperation in ad hoc networks”
– formulated a model and meta-model using game theory
– introduced the concept of dependencies / dependency graph
– study of NE
• in theory, NE based on cooperation exist
• in practice, the necessary conditions for cooperation do not hold
–
►
showed that part of the network can still cooperate
Ch. 4: Packet forwarding in dynamic ad-hoc networks
“mobility helps cooperation in ad hoc networks”
– spontaneous cooperation exists on a ring scenario (theoretical)
– cooperation resistant to drift (alternative cooperative strategies) to some
extent
– in reality, generosity is needed
– as mobility increases, less generosity is needed
►
Ch. 5: Packet forwarding in multi-domain sensor networks
“sharing sinks is beneficial and sharing sensors is also in certain scenarios”
– energy saving gives a natural incentive for cooperation
• sharing sinks
• if sinks are common resources, then sharing sensors is worth in sparse networks
April 2007
Márk Félegyházi (EPFL) - PhD defense
64
Thesis contributions (3/3)
►
Ch. 6: Cellular operators in a shared spectrum
“both cooperation (low powers) and defection (high powers) exist, but
cooperation can be enforced by punishments”
– wireless operators compete in a shared spectrum
– single stage game
• various Nash equilibria in the grid scenario, depending on cooperation
parameters
–
repeated game
• RMIN (cooperation) is enforceable with punishments
–
general scenario = arbitrary ranges
• the problem is NP-complete
►
Ch. 7: Border games in cellular networks
“operators have an incentive to adjust their pilot power on the borders”
– competitive power control on a national border
– formulated a power control game
• operators have an incentive to be strategic
• NE are efficient, but they use high power
–
–
April 2007
proposed a simple convergence algorithm
extended game corresponds to the Prisoner’s Dilemma
Márk Félegyházi (EPFL) - PhD defense
65