Non-Cooperative Behavior in Wireless Networks

Non-Cooperative Behavior

in Wireless Networks

Márk Félegyházi (EPFL)

PhD. defense – April 2007

April 2007 Márk Félegyházi (EPFL) - PhD defense 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


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

TR

EN

DS

OU

TC

OM

E

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, Čagalj et al. 2005]

– Wi-Fi pricing [Musacchio and Walrand 2004/2006]


Outline of the thesis

► 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 I: Introduction to game theory

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, 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]


Problem

► multi-radio devices► set of available channels

How to assign radios to available channels?

3d4d5d

6d

1d 2d


System model (1/3)

3d4d5d

6d

1d 2d

2p

1p

3p

► – set of orthogonal channels (|| = C)

► – set of communicating pairs of devices (|| = 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► τ() – 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)

,i xknumber of links by pair i on channel x→

,i i xx C

k k

,x i xi N

k k

example:

3 2, 2p ck

multiple communication links on one channel ?

, 1i xk Intuition:

23ck

34pk


► selfish users (communicating pairs)► non-cooperative game GCA

– players → communicating pairs – strategy → channel allocation – payoff → total throughput

► strategy:

► strategy matrix:

► payoff:

Multi-radio channel allocation (CA) game

,1 ,,...,i i i Cs k k

1

N

s

S

s

, ( )i xi i x

x C x

ku k

k


Lemma: If S* is a NE in GCA, then .

Use of all radios

Each player should use all of his radios.

p4 p4

,ik k i

Intuition: Player i is always better of deploying unused radios.

all channel allocations

Lem

ma


Proposition: If S* is a NE in GCA, then dy,x ≤ 1, for any channel x and y.

Load-balancing channel allocation

► Consider two arbitrary channels x and y, where ky ≥ kx

► distance: dy,x = ky – kx

NE candidate:


Lem

ma

Pro

posi

tion


Nash equilibria (1/2)

Theorem (case 1): If for any two channels x and y in it is true that ki,x ≤ 1, for all i and dy,x ≤ 1, then S* is a Nash equilibrium.

p2

Nash Equilibrium:

Use one link per channel.


► distance: dy,x = ky – kx

p4


Lem

ma

Pro

posi

tion NE case 1


Theorem (case 2): If dy,x ≤ 1 for x,y in C and there exists j in 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 equilibria (2/2)

Nash Equilibrium:

minC

channels with the minimum/maximum

number of links→

dy,x = ky – kx

di,y,x = ki,y – ki,x

maxC

Use multiple links on certain channels.


Lem

ma

Pro

posi

tion NE case 1

NE case 2


Efficiency (1/2)

1

1 1 1x x x x

POAN k

k k k kC

Corollary: If the throughput function τ() is constant (ex. theoretical CSMA/CA), then any Nash equilibrium channel allocation is Pareto-optimal in GCA.

Theorem: In GCA, the price of anarchy is:

, 1x x

N k N kk k

C C

where


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


Convergence to NE (1/3)

p1 p1

N = 5, C = 6, k = 3

p2 p2

p4

p1

p3 p2 p5

p4

p5

p3

p3

p4

p5

c1 c2 c3c4 c5 c6

timep5: c2→c5

c6→c4p3: c2→c5

c6→c4c1→c3

p2: c2→c5p1: c2→c5

c6→c4

p1: c4→c6c5→c2

p4: idle

channelsp5

p3

p2

p1

p1

p4

Algorithm with imperfect info:► move links from “crowded”

channels to other randomly chosen channels

► desynchronize the changes► convergence is not ensured



3UB

Algorithm with imperfect info:► move links from “crowded”

channels to other randomly chosen channels

► desynchronize the changes► convergence is not ensured

xx

N kS k

C

C

Balance:

unbalanced (UB): best balance (NE):

Efficiency: ( ) ( )

( ) ( )UB

UB NE

S SS

S S

0 1S

15UB 7S

15 7 3

15 3 4S



N (# of pairs) 10

C (# of channels) 8

k (radios per device) 3

τ(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-CooperativeNetwork 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 controlUsers:► roaming users► users uniformly distributed► select the best quality BS► selection based signal-to-

interference-plus-noise ratio (SINR)


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

Mtr 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


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


Simulation


Is there a game?

► only A is strategic (B uses PB = PS)► 10 data users ► path loss exponent, α = 2

Δi


Strategic advantage

max , ,

,i

S S Si i i

si S S

i

u s P u P P

u P P

► normalized payoff difference:


Payoff of A

► Both operators are strategic► path loss exponent, α = 4


Nash equilibrium

► unique NE► NE power P* is higher than PS


Efficiency

► 10 data users zero-sum game


► 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

– Prisoner’s 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

3d4d5d

6d

1d 2d

2p

1p

3p

► 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. 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


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

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


Selected publications (à la Prof. Gallager)

► M. Félegyházi, M. Čagalj, S. S. Bidokhti, and J.-P. Hubaux, “Non-Cooperative 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


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



► 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



► 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 = (, , )– – players: p1 and p2

– – strategies: choosing the channels• and

– – payoff functions: received throughputs• and

13c

c1 c2

f1 f2 f3

22c

11 pu 22 pu

1 1 2{ , }s c c 2 1 2{ , }s c c is S strategy of player i

iu U payoff of player i1 2( , )s s s strategy profile


Strategic form

► the CA game in strategic form

p2

c1 c2

p1

c1 1.5,1.5 3,2

c2 2,3 1,1

13c

22c


Stability: Nash Equilibrium

p2

c1 c2

p1

c1 1.5,1.5 3,2

c2 2,3 1,1

13c

22c

Nash equilibrium: No player has an incentive to unilaterally deviate.* * *( , ) ( , ),i i i i i i iu s s u s s s S

Best response: Best strategy of player i given the strategies of others.

' '( ) : ( , ) ( , ),i i i i i i i i i ibr s s u s s u s s s S S


Efficiency: Pareto-Optimality

p2

c1 c2

p1

c1 1.5,1.5 3,2

c2 2,3 1,1

13c

22c

Price of anarchy: The ratio between the total payoff of players playing a socially-optimal (max. Pareto-optimal) strategy and a worst Nash equilibrium.

soi

iw NEi

i

uPOA

u

Pareto-optimality: The strategy profile spo is Pareto-optimal if:

' ': ( ) ( ),poi is u s u s i with strict inequality for at least one player i


Fairness

Nash equilibria (case 1) Nash equilibria (case 2)fair unfair

Theorem: A NE channel allocation S* is max-min fair iff

min min

, , , ,i x j xx x

k k i j

C C

N

Intuition: This implies equality: ui = uj, i,j


Centralized algorithm

Assign links to the channels sequentially.

p1 p1 p1p1 p2p2

p2p2 p3 p3 p3p3

p4 p4 p4p4


► basic elements of DS-CDMA:

► UMTS parameters:

System model UMTS

D. Tse and P. Viswanath, “Fundamentals of Wireless Communication,” Cambride Univ. Press, 2005H. Holma and A. Toskala, eds. “WCDMA for UMTS,” John Wiley & Sons, Inc., 2002

channelencoder

modulator channel demodulatorchanneldecoder

PR patterngenerator

PR patterngenerator

inputdata

outputdata

requiredSINR

requiredCIR


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

► M users in total► cost for high power C► payoff difference Δ

p2

PS P*

p1

PS M/2, M/2M/2-Δ,

M/2+Δ-C

P* M/2+Δ-C, M/2-Δ

M/2-C, M/2-C

p2

PS P*

p1

PS 5, 5 3, 6

P* 6, 3 4, 4

Prisoner’s Dilemma► M = 10► C = 1► Δ = 2


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 Prisoner’s Dilemma

Documents

Non-Cooperative Behavior in Wireless Networks