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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
- 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

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?

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

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

Part II Non-Cooperative Users

- Chapter 2
- Multi-Radio Channel Allocation in Wireless

Networks

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

Problem

- multi-radio devices
- set of available channels

How to assign radios to available channels?

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

System model (2/3)

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

1

number of links

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 ?

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

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

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

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

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

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.

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

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

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

Convergence to NE (3/3)

N ( of pairs) 10

C ( of channels) 8

k (radios per device) 3

t(1) (max. throughput) 54 Mbps

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

Part III Non-Cooperative Network Operators

- Chapter 7
- Border Games in Cellular Networks

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

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?

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)

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

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

Simulation

Is there a game?

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

?i

Strategic advantage

- normalized payoff difference

Payoff of A

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

Nash equilibrium

- unique NE
- NE power P is higher than PS

Efficiency

zero-sum game

- 10 data users

Convergence to NE (1/2)

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

PA 6.5 W

Convergence to NE (2/2)

- convergence step 0.1 W

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

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

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

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

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

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

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

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

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

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

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

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

Extensions

Introduction to Game Theory

- Chapter 1
- A Tutorial on Game Theory

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

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

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

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

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

Centralized algorithm

Assign links to the channels sequentially.

p4

p4

p4

p4

p2

p2

p3

p3

p3

p3

p2

p1

p1

p1

p1

p2

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

Nash equilibrium (2/2)

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

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

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

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

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

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