Non-Cooperative Behavior in Wireless Networks

1
Non-Cooperative Behavior in Wireless Networks

• Márk Félegyházi (EPFL)

PhD. defense April 2007
2
Prospective wireless networks

• Relaxing spectrum licensing
• small network operators in unlicensed bands
• inexpensive access points
• flexible deployment
• community and ad hoc networks
• no authority
• peer-to-peer network operation
• cognitive radio
• restricted operation in any frequency band
• no interference with licensed (primary) users
• adaptive behavior

3
Motivation

• more complexity at the network edges
• decentralization
• ease of programming for wireless devices
• rational users
• ?
• more adaptive wireless devices
• potential selfish behavior of devices

TRENDS
OUTCOME
What is the effect of selfish behavior in
wireless networks?
4
Game theory in networking

• Peer-to-peer networks
• free-riding Golle et al. 2001, Feldman et al.
  2007
• trust modeling Aberer et al. 2006
• Wired networks
• 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
• 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, Cagalj et al. 2005
• Wi-Fi pricing Musacchio and Walrand 2004/2006

5
Outline of the thesis
Part I Introduction to game theory

• 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

Part II Non-cooperative users
Part III Non-cooperative network operators
6
Part II Non-Cooperative Users

• Chapter 2
• Multi-Radio Channel Allocation in Wireless
  Networks

7
Related Work

• Channel allocation
• 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
• Multi-radio networks
• mesh networks Adya et al. 2004, Alicherry et al.
  2005
• cognitive radio So et al. 2005
• Competitive medium access
• Aloha MacKenzie and Wicker 2003, Yuen and
  Marbach 2005
• CSMA/CA Konorski 2002, Cagalj et al. 2005
• WLAN channel coloring Halldórsson et al. 2004
• channel allocation in cognitive radio networks
  Cao and Zheng 2005, Nie and Comaniciu 2005

8
Problem

• multi-radio devices
• set of available channels

How to assign radios to available channels?
9
System model (1/3)

• 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

10
System model (2/3)

• channels with the same properties
• t() total throughput on any channel x

1
number of links
11
System model (3/3)

• N communicating pairs of devices
• C orthogonal channels
• k radios at each device (k links for each pair)

number of links by pair i on channel x
?
Intuition
example
multiple communication links on one channel ?
12
Multi-radio channel allocation (CA) game

• selfish users (communicating pairs)
• non-cooperative game GCA
• players ? communicating pairs
• strategy ? channel allocation
• payoff ? total throughput
• strategy
• strategy matrix
• payoff

13
Use of all radios
Lemma If S is a NE in GCA, then .
Each player should use all of his radios.
Intuition Player i is always better of deploying
unused radios.
all channel allocations
Lemma
14
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
all channel allocations
Lemma
Proposition
15
Nash equilibria (1/2)

• Consider two arbitrary channels x and y, where ky
  kx
• distance dy,x ky kx

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.
all channel allocations
NE case 1
Lemma
Proposition
16
Nash equilibria (2/2)

• Consider two arbitrary channels x and y, where ky
  kx

channels with the minimum/maximum number of links
dy,x ky kx di,y,x ki,y ki,x
?
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 gt 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.
Use multiple links on certain channels.
Nash Equilibrium
all channel allocations
NE case 1
Lemma
Proposition
NE case 2
17
Efficiency (1/2)
Theorem In GCA, the price of anarchy is
where
Corollary If the throughput function t() is
constant (ex. theoretical CSMA/CA), then any Nash
equilibrium channel allocation is Pareto-optimal
in GCA.
18
Efficiency (2/2)

• CSMA/CA protocol
• In theory, the throughput function t() is
  constant ? POA 1
• In practice, there are collisions, but t()
  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), 183, Mar. 2000
19
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

N 5, C 6, k 3
p5
p4
p5
p4
p3
p4
p3
p2
p5
p3
p1
p1
p2
p2
p1
time
p5 c2?c5
p1 c4?c6
c4
c5
channels
c1
c2
c3
c6
p1
p5
c6?c4
c5?c2
p4
p3
p3 c2?c5
p4 idle
p2
c6?c4
c1?c3
p1
p2 c2?c5
p1 c2?c5
c6?c4
20
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

Balance
best balance (NE)
unbalanced (UB)
Efficiency
21
Convergence to NE (3/3)
N ( of pairs) 10
C ( of channels) 8
k (radios per device) 3
t(1) (max. throughput) 54 Mbps
22
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
• players should use all their radios
• load-balancing channel allocation
• two cases of Nash equilibria
• NE are efficient both in theory and practice
• fairness issues
• coalition-proof equilibria
• algorithms to achieve efficient NE
• centralized algorithm with perfect information
• distributed algorithm with imperfect information

23
Part III Non-CooperativeNetwork Operators

• Chapter 7
• Border Games in Cellular Networks

24
Related Work

• Power control in cellular networks
• 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
• Coexistence of service providers
• wired Shakkottai and Srikant 2005, He and
  Walrand 2006
• wireless Shakkottai et al. 2006, Zemlianov and
  de Veciana 2005

25
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?
26
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)

27
System model (2/2)
TAw
pilot signal SINR
TBw
TAv
PB
PA
B
v
A
Pi pilot power of i
processing gain for the pilot signal
channel gain between BS i and user v
traffic signal SINR
noise energy per symbol
available bandwidth
own-cell interference affecting the pilot signal
own-cell interference factor
traffic power between BS i and user v
set of users attached to BS i
other-to-own-cell interference factor
28
Game-theoretic model

• Power Control Game, GPC
• players ? networks operators (BSs), A and B
• strategy ? pilot signal power, 0W lt Pi lt 10W, i
  A, B
• standard power, PS 2W
• payoff ? profit, where is
  the expected income serving user v
• normalized payoff difference

29
Simulation
30
Is there a game?

• only A is strategic (B uses PB PS)
• 10 data users
• path loss exponent, a 2

?i
31
Strategic advantage

• normalized payoff difference

32
Payoff of A

• Both operators are strategic
• path loss exponent, a 4

33
Nash equilibrium

• unique NE
• NE power P is higher than PS

34
Efficiency
zero-sum game

• 10 data users

35
Convergence to NE (1/2)

• convergence based on better-response dynamics
• convergence step 2 W

PA 6.5 W
36
Convergence to NE (2/2)

• convergence step 0.1 W

37
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
• Prisoners Dilemma

38
Summary
39
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
40
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

• 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
• fairness issues
• coalition-proof equilibria
• convergence algorithms to efficient NE

M. Félegyházi, M. Cagalj, 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
41
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
42
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
43
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
44
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
• 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

M. Félegyházi and J.-P. Hubaux, Wireless
Operators in a Shared Spectrum, in Proceedings
of Infocom 2006, Barcelona, Spain, April 23-29,
2006
45
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 Prisoners
  Dilemma

M. Félegyházi, M. Cagalj, D. Dufour, and J.-P.
Hubaux, Border Games in Cellular Networks, in
Proceedings of Infocom 2007, Anchorage, USA, May
6-12, 2007
46
Selected publications (à la Prof. Gallager)

• M. Félegyházi, M. Cagalj, S. S. Bidokhti, and
  J.-P. Hubaux, Non-Cooperative Multi-Radio
  Channel Allocation in Wireless Networks, in
  Infocom 2007
• M. Félegyházi, M. Cagalj, 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

47
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. Cagalj and J.-P.
Hubaux, Efficient MAC in Cognitive Radio
Systems A Game-Theoretic Approach, submitted to
IEEE JSAC, Special Issue on Cognitive Radios, 2008
48
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
49
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
50
Extensions
51
Introduction to Game Theory

• Chapter 1
• A Tutorial on Game Theory

52
The Channel Allocation Game

• two channels c1 and c2
• total available throughput and
• two devices p1 and p2
• throughput is fairly shared
• users of the devices are rational
• ?
• Channel Allocation (CA) Game GCA (N, S, U)
• N players p1 and p2
• S strategies choosing the channels
• and
• U payoff functions received throughputs
• and

strategy of player i
strategy profile
payoff of player i
53
Strategic form

• the CA game in strategic form

p2 p2
c1 c2
p1 c1 1.5,1.5 3,2
p1 c2 2,3 1,1
54
Stability Nash Equilibrium
Best response Best strategy of player i given
the strategies of others.
Nash equilibrium No player has an incentive to
unilaterally deviate.
p2 p2
c1 c2
p1 c1 1.5,1.5 3,2
p1 c2 2,3 1,1
55
Efficiency Pareto-Optimality
Pareto-optimality The strategy profile spo is
Pareto-optimal if
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.
p2 p2
c1 c2
p1 c1 1.5,1.5 3,2
p1 c2 2,3 1,1
56
Fairness
Nash equilibria (case 2)
Nash equilibria (case 1)
unfair
fair
Theorem A NE channel allocation S is max-min
fair iff
Intuition This implies equality ui uj, ?i,j ?
N
57
Centralized algorithm
Assign links to the channels sequentially.
p4
p4
p4
p4
p2
p2
p3
p3
p3
p3
p2
p1
p1
p1
p1
p2
58
System model UMTS

• basic elements of DS-CDMA
• UMTS parameters

required SINR
required CIR
input data
output data
channel encoder
channel
demodulator
channel decoder
modulator
PR pattern generator
PR pattern generator
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
59
Nash equilibrium (2/2)
60
Efficiency (2/2)
Price of conformance Ratio between the total
payoff in a Pareto-optimal strategy profile and
the one using the standard power, PS
61
Extended Game with Power Costs

• Prisoners Dilemma
• M 10
• C 1
• ? 2

• M users in total
• cost for high power C
• payoff difference ?

p2 p2
PS P
p1 PS 5, 5 3, 6
p1 P 6, 3 4, 4
p2 p2
PS P
p1 PS M/2, M/2 M/2-?, M/2?-C
p1 P M/2?-C, M/2-? M/2-C, M/2-C
62
Thesis contributions

• Ch 1 A tutorial on game theory
• facilitate the application of game theory in
  wireless networks
• 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
• Ch. 3 Packet forwarding in static ad-hoc
  networks
• incentives are needed to promote cooperation in
  ad hoc networks
• Ch. 4 Packet forwarding in dynamic ad-hoc
  networks
• mobility helps cooperation in ad hoc networks
• Ch. 5 Packet forwarding in multi-domain sensor
  networks
• sharing sinks is beneficial and sharing sensors
  is also in certain scenarios
• Ch. 6 Cellular operators in a shared spectrum
• both cooperation (low powers) and defection (high
  powers) exist, but cooperation can be enforced by
  punishments
• Ch. 7 Border games in cellular networks
• operators have an incentive to adjust their pilot
  power on the borders

63
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
• centralized algorithm with perfect information
• distributed algorithm with perfect information
• distributed algorithm with imperfect information
• proof of convergence for each algorithm
• coalition-proof equilibria

64
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

65
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
• proposed a simple convergence algorithm
• extended game corresponds to the Prisoners
  Dilemma