Non-Cooperative Behavior
in Wireless Networks
Márk Félegyházi (EPFL)
May 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
–
–
–
May 2007
inexpensive access points
flexible deployment
restricted operation in any frequency band
no interference with licensed (primary) users
adaptive behavior
Márk Félegyházi (EPFL)
2
Motivation
TRENDS
►
►
►
OUTCOME
►
►
►
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?
May 2007
Márk Félegyházi (EPFL)
3
Related work (1/2)
►
Peer-to-peer networks
–
–
►
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
–
–
–
–
May 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)
4
Related work (2/2)
Security
Cooperation
12. Behavior enforcement
8. Privacy protection
11. Operators in shared spectrum
7. Secure routing
10. Selfishness in PKT FWing
6. Secure neighbor discovery
5. Security associations
9. Selfishness at the MAC layer
4. Naming and addressing
3. Trust
Appendix A:
Security and crypto 2. Upcoming networks
1. Existing networks
http://secowinet.epfl.ch
May 2007
Appendix B:
Game theory
Márk Félegyházi (EPFL)
5
Summary of my research
Part I:
Introduction to game theory
►
►
Part II:
Non-cooperative users
►
►
Part III:
Non-cooperative network
operators
May 2007
►
►
►
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)
6
Introduction to Game Theory
The channel allocation (CA) game
►
two channels: c1 and c2
–
►
►
►
►
total available throughput:  ct  3 and  ct2  2
1
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
•
May 2007
s1  {c1 , c2 } and s2  {c1 , c2 }
u1   p1 and u2   p2
Márk Félegyházi (EPFL)
si  S strategy of player i
s  (s1 , s2 ) strategy profile
ui  U payoff of player i
8
Strategic form
►
the CA game in strategic form
p2
p1
May 2007
c1
c2
c1
1.5,1.5
3,2
 ct  3
c2
2,3
1,1
 ct  2
Márk Félegyházi (EPFL)
1
2
9
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
May 2007
c1
c2
c1
c2
1.5,1.5
3,2
 ct  3
1,1
 ct  2
2,3
Márk Félegyházi (EPFL)
1
2
10
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
1.5,1.5
3,2
 ct  3
1,1
 ct  2
i
p1
May 2007
c1
c2
2,3
Márk Félegyházi (EPFL)
1
2
11
Multi-Radio Channel Allocation
in Wireless Networks
Non-Cooperative Users
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
–
–
–
–
May 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)
13
Problem
d2
d1
►
►
multi-radio devices
set of available channels
d5
d4
d3
d6
How to assign radios to available channels?
May 2007
Márk Félegyházi (EPFL)
14
System model (1/3)
►
►
►
►
►
►
C – set of orthogonal
channels (|C| = C)
N – set of communicating
pairs of devices (|N| = N)
sender controls the
communication (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
May 2007
p1
d2
d1
d5
d4
d3
Márk Félegyházi (EPFL)
p2
p3
d6
15
System model (2/3)
►
►
►
N communicating pairs of devices
C orthogonal channels
k radios at each device
ki , x→
number of radios
by sender i
on channel x
ki   ki , x
xC
k x   ki , x
example:
Intuition: ki , x  1
iN
kc2  3
Use multiple radios on one channel ? k p  4
3
k p3 ,c2  2
May 2007
Márk Félegyházi (EPFL)
16
System model (3/3)
►
►
►
May 2007
channels with the same properties
τ t(kx) – total throughput on any channel x
τ(kx) – throughput per radio
Márk Félegyházi (EPFL)
17
Multi-radio channel allocation (MRCA) game
►
►
selfish users (communicating pairs)
non-cooperative game GMRCA
– players → senders
– strategy → channel allocation
– payoff → total throughput
si  ki ,1 ,..., ki ,C 
►
strategy:
►
strategy matrix:
►
payoff:
 s1 
 
S    
s 
 N
ui   i    ki , x  (k x ) 
xC
May 2007
Márk Félegyházi (EPFL)
18
Use of all radios
Lemma: If S* is a NE in GMRCA, then ki  k , i.
Each player should use all of his radios.
Intuition: Player i is always better off deploying unused
radios.
p4 p4
Lemma
all channel allocations
May 2007
Márk Félegyházi (EPFL)
19
Load-balancing channel allocation
►
►
Consider two arbitrary channels x and y in C, where kx ≥ ky
distance: dx,y = kx – ky
Proposition: If S* is a NE in GMRCA, then dy,x ≤ 1, for any
channel x and y.
Proposition
Lemma
all channel allocations
May 2007
Márk Félegyházi (EPFL)
20
Nash equilibria (1/2)
►
►
Consider two arbitrary channels x and y in C, where kx ≥ ky
distance: dx,y = kx – ky
Theorem 1: A channel allocation S* is a Nash equilibrium in GMRCA
if for all i:
► dx,y ≤ 1 and
► ki,x ≤ 1.
Nash
Equilibrium:
Use one radiop4per channel.
p2
Proposition
Lemma
all channel allocations
May 2007
NE type 1
Márk Félegyházi (EPFL)
21
Nash equilibria (2/2)
►
►
►
Consider two arbitrary channels x and y in C, where kx ≥ ky
distance: dx,y = kx – ky
loaded and less loaded channels: C+ and C–
Theorem 2: A channel allocation S* is a Nash equilibrium in GMRCA if:
► dx,y ≤ 1,
 (k x  1)   (k x  1)
► for any player i who has ki,x ≥ 2, x in C, ki , x 
 (k x  1)   (k x )
+
► for any player i who has ki,x ≥ 2 and x in C , ki,y ≥ ki,x – 1, for all y in
C–
Nash
Equilibrium:
Proposition
Lemma
all channel allocations
Use multiple radios
on certain channels.
NE type 1
May 2007 NE type 2
– Félegyházi (EPFL)
CMárk
C+
22
Efficiency (1/2)
Theorem: In GMRCA , the price of anarchy is:
POA 
 t 1
N k  t

t
t
k

1



k


k

1






 k x  1
 x

x
x
C 



 N k 
 N k 
, kx  1  
where k x  


C
C




Corollary: If τt(kx) is constant (i.e., ideal TDMA), then any
Nash equilibrium channel allocation is Pareto-optimal in
GMRCA.
May 2007
Márk Félegyházi (EPFL)
23
Efficiency (2/2)
►
►
In theory, if the total throughput function τt(kx) is constant  POA = 1
In practice, there are collisions, but τt(kx) 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
May 2007
Márk Félegyházi (EPFL)
24
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
May 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
Márk Félegyházi (EPFL)
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
p
1
25
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
May 2007
Márk Félegyházi (EPFL)
26
Convergence to NE (3/3)
N (# of pairs)
10
C (# of channels)
8
k (radios per device)
3
τ(1) (max. throughput) 54 Mbps
May 2007
Márk Félegyházi (EPFL)
27
Summary and Future Work
Summary – Multi-radio channel allocation
►
►
►
►
wireless networks with multi-radio devices
users of the devices are selfish players
GMRCA – multi-radio channel allocation game
results for a Nash equilibrium:
–
–
–
–
►
►
►
fairness issues
coalition-proof equilibria
algorithms to achieve efficient NE:
–
–
May 2007
players should use all their radios
load-balancing channel allocation
two types of Nash equilibria
NE are efficient both in theory and practice
centralized algorithm with perfect information
distributed algorithm with imperfect information
Márk Félegyházi (EPFL)
29
Summary of my research
Part I:
Introduction to game theory
►
►
Part II:
Non-cooperative users
►
►
Part III:
Non-cooperative network
operators
May 2007
►
►
►
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)
30
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
May 2007
Márk Félegyházi (EPFL)
31
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”
May 2007
Márk Félegyházi (EPFL)
32
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”
May 2007
Márk Félegyházi (EPFL)
33
Extensions
My research
Non-cooperative users
►
►
►
Multi-radio channel allocation in wireless networks
Packet forwarding in static ad-hoc networks
Packet forwarding in dynamic ad-hoc networks
Non-cooperative network operators
►
►
►
May 2007
Packet forwarding in multi-domain sensor networks
Cellular operators in a shared spectrum
Border games in cellular networks
Márk Félegyházi (EPFL)
35
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
May 2007
Márk Félegyházi (EPFL)
36
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
May 2007
Márk Félegyházi (EPFL)
37
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
May 2007
Márk Félegyházi (EPFL)
38
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
May 2007
Márk Félegyházi (EPFL)
39
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
May 2007
Márk Félegyházi (EPFL)
40
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
May 2007
Márk Félegyházi (EPFL)
41
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
May 2007
Márk Félegyházi (EPFL)
42
Selected publications
(à la Prof. Gallager)
►
►
►
May 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)
43
Fairness
Nash equilibria (fair)
Nash equilibria (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
May 2007
Márk Félegyházi (EPFL)
44
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
May 2007
4
p
Márk Félegyházi (EPFL)
45
Thesis contributions
►
Ch 1: A tutorial on game theory
–
►
Ch. 2: Multi-radio channel allocation 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
–
May 2007
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
operators have an incentive to adjust their pilot power on the borders
Márk Félegyházi (EPFL)
46