Non-Cooperative Behavior in Wireless Networks Márk Félegyházi (EPFL) May 2007.

Non-Cooperative Behavior

in Wireless Networks

Márk Félegyházi (EPFL)

May 2007

May 2007 Márk Félegyházi (EPFL) 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?


Related work (1/2)► 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]


http://secowinet.epfl.ch

Related work (2/2)

1. Existing networks

2. Upcoming networks

3. Trust

4. Naming and addressing

5. Security associations

6. Secure neighbor discovery

7. Secure routing

8. Privacy protection

10. Selfishness in PKT FWing

11. Operators in shared spectrum

12. Behavior enforcement

Appendix A:Security and crypto

Appendix B:Game theory

Security Cooperation

9. Selfishness at the MAC layer


Summary of my research

► 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

Introduction to Game Theory


The channel allocation (CA) 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

13t

c

c1 c2

f1 f2 f3

22t

c

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

13t

c

22t

c


Stability: Nash equilibrium

p2

c1 c2

p1

c1 1.5,1.5 3,2

c2 2,3 1,1

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

13t

c

22t

c


Efficiency: Pareto-optimality

p2

c1 c2

p1

c1 1.5,1.5 3,2

c2 2,3 1,1

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

13t

c

22t

c

Multi-Radio Channel Allocation in Wireless Networks

Non-Cooperative Users


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 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


System model (2/3)

► N communicating pairs of devices► C orthogonal channels► k radios at each device

,i xknumber of radios

by sender i on channel x

→

,i i xx C

k k

,x i xi N

k k

example:

3 2, 2p ck

Use multiple radios on one channel ?

, 1i xk Intuition:

23ck

34pk


System model (3/3)► channels with the same properties► τ t(kx) – total throughput on any channel x

► τ(kx) – throughput per radio


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

– players → senders – strategy → channel allocation – payoff → total throughput

► strategy:

► strategy matrix:

► payoff:

Multi-radio channel allocation (MRCA) game

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

1

N

s

S

s

, ( )i i i x xx C

u k k


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

Use of all radios

Each player should use all of his radios.

p4 p4

,ik k i

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

all channel allocations

Lem

ma


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

Load-balancing channel allocation► Consider two arbitrary channels x and y in , where kx ≥ ky► distance: dx,y = kx – ky


Lem

ma

Pro

posi

tion


Nash equilibria (1/2)

Theorem 1: A channel allocation S* is a Nash equilibrium in GMRCA if for all i:

► dx,y ≤ 1 and

► ki,x ≤ 1.

p2

Nash Equilibrium: p4

Use one radio per channel.


Lem

ma

Pro

posi

tion NE type 1

► Consider two arbitrary channels x and y in , where kx ≥ ky► distance: dx,y = kx – ky


Nash equilibria (2/2)

Nash Equilibrium:

Theorem 2: A channel allocation S* is a Nash equilibrium in GMRCA if:

► dx,y ≤ 1,

► for any player i who has ki,x ≥ 2, x in ,

► for any player i who has ki,x ≥ 2 and x in +, ki,y ≥ ki,x – 1, for all y in –

Use multiple radios on certain channels.all channel allocations

Lem

ma

Pro

posi

tion NE type 1

NE type 2

,

( 1) ( 1)

( 1) ( )x x

i xx x

k kk

k k

► Consider two arbitrary channels x and y in , where kx ≥ ky► distance: dx,y = kx – ky

► loaded and less loaded channels: + and –

+–


Efficiency (1/2)

1

1 1 1

t

t t tx x x x

POAN k

k k k kC

Corollary: If τt(kx) is constant (i.e., ideal TDMA), then any Nash equilibrium channel allocation is Pareto-optimal in GMRCA.

Theorem: In GMRCA , the price of anarchy is:

, 1x x

N k N kk k

C C

where


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


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 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:

– players should use all their radios– load-balancing channel allocation– two types 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


Summary of my research

► 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


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”



► 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”

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 networksNon-cooperative network operators► Packet forwarding in multi-domain sensor networks► Cellular operators in a shared spectrum► Border games in cellular networks


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


Fairness

Nash equilibria (fair) Nash equilibria (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


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

Non-Cooperative Behavior in Wireless Networks Márk Félegyházi (EPFL) May 2007.

Documents

cellular networks

existing networks

upcoming networks

game theory slide

multidomain sensor networks

mac layer slide

noncooperative behavior

shared users