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Chapter 10: Selfishness in packet forwarding

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Chapter 10: Selfishness in packet forwarding. Introduction. the operation of multi-hop wireless networks requires the nodes to forward data packets on behalf of other nodes - PowerPoint PPT Presentation
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007 Levente Buttyán and Jean-Pierre Hubaux Security and Cooperation in Wireless Networks http://secowinet.epfl.ch/ Chapter 10: Selfishness in packet forwarding
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Page 1: Chapter 10: Selfishness in packet forwarding

© 2007 Levente Buttyán and Jean-Pierre Hubaux

Security and Cooperation in Wireless Networks

http://secowinet.epfl.ch/

Chapter 10: Selfishness in packet forwarding

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2/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding

Introduction

the operation of multi-hop wireless networks requires the nodes to forward data packets on behalf of other nodes

however, such cooperative behavior has no direct benefit for the forwarding node, and it consumes valuable resources (battery)

hence, the nodes may tend to behave selfishly and deny cooperation

if many nodes defect, then the operation of the entire network is jeopardized

questions:– What are the conditions for the emergence of cooperation in

packet forwarding?– Can it emerge spontaneously or should it be stimulated by

some external mechanism?

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Modeling packet forwarding as a game

time0

time slot:

1 t

Strategy: cooperation level

mC(0) mC(1) mC(t)

Players: nodes

Benefit (of node i): proportion of packets sent by node i reaching their destination

10.1 Game theoretic model of packet forwarding

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Cost function

ˆ, ( ) ,jf s jc r t T r C r t

Cost for forwarder fj :

where: Ts(r) – traffic sent by source s on route r C – unit cost of forwarding

Example :

{ , }

ˆ , ( ) ( ) ( )kC f E C

k E C

r t m t m t m t

ˆ, ( ) ,C A jc r t T r C r t

A E C D

TAmE(t) mC(t)

r (A→D):

10.1 Game theoretic model of packet forwarding

1

ˆ , ( )k

j

j fk

r t m t

Normalized throughput at forwarder fj :

where: r – route on which fk is a forwarder t – time slot fk – forwarders on route r mfk – cooperation level of forwarder fk

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Benefit function

, ( ) ( ) ( )A E Cr t T r m t m t

1

, ( ) ( )k

l

s fk

r t T r m t

where: s – sourcer – route on which s is a sourcet – time slotfk – forwarders for spfk – cooperation level of forwarder fk

Experienced throughput :

A E C D

TAmE(t) mC(t)

r (A→D):

Example :

benefit function :

10.1 Game theoretic model of packet forwarding

bS

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Total payoff

( ) ( )

, ,i i

i i iq S t r F t

u t b q t c r t

The goal of each node is to maximize its total payoff over the game:

Payoff = Benefit - Cost

where: Si(t) – set of routes on which i is a source Fi(t) – set of routes on which i is a forwarder

0

ti

t

u t

where: – discounting factort – time

time0time slot: 1 t

Payoff: uA(0) uA(1). uA(t). t

Example :

10.1 Game theoretic model of packet forwarding

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Representation of the nodes as players

Node i is playing against the rest

of the network (represented by the

box denoted by A-i )

yi

xi

A-i i ( ) ([ ( , 1)])iim t r t

Strategy function for node i:

where:

(r,t) – experienced throughput

10.1 Game theoretic model of packet forwarding

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Examples of strategies

1)( ii y

iii xy )(

0)( ii y

StrategyFunction

Initial cooperation

level

AllD (always defect)

AllC (always cooperate)

TFT (Tit-For-Tat)

0

1

1

non-reactive strategies: the output of the strategy functionis independent of the input (example: AllD and AllC)

reactive strategies: the output of the strategy functiondepends on the input (example: TFT)

where yi stands for the input

iii yy )(

10.1 Game theoretic model of packet forwarding

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Concept of dependency graph

dependency: the benefit of each source is dependent on the behavior of its forwarders

dependency loop

10.2 Meta-model

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10/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding

Analytical Results (1/2)

0)( IF

Theorem 1: If node i does not have any dependency loops, then its best strategy is AllD.

Theorem 2: If node i has only non-reactive dependency loops, then its best strategy is AllD.

Corollary 1: If every node plays AllD, it is a Nash-equilibrium. Corollary 1: If every node plays AllD, it is a Nash-equilibrium.

0)( IE

node i

node playing a non-reactive strategy

other nodes

10.3 Analytical results

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Analytical results (2/2)

Corollary 2: If Theorem 3 holds for every node, it is a Nash-equilibrium.Corollary 2: If Theorem 3 holds for every node, it is a Nash-equilibrium.

Theorem 3 (simplified): Assuming that node i is a forwarder, its behavior will be cooperative only if it has a dependency loop with each of its sources

Theorem 3 (simplified): Assuming that node i is a forwarder, its behavior will be cooperative only if it has a dependency loop with each of its sources

Example in which Corollary 2 holds:

A B

C

A B

C

Network Dependency graph

10.3 Analytical results

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Classification of scenarios

D: Set of scenarios, in which every node playing AllD is a Nash equilibrium

C: Set of scenarios, in which a Nash equilibrium based on cooperation is not

excluded by Theorem 1

C2: Set of scenarios, in which cooperation is based on the conditions expressed in

Corollary 2

10.3 Analytical results

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Simulation settings

Number of nodes 100, 150, 200

Area type torus

Area size 1500x1500m, 1850x1850m, 2150x2150m

Radio range 200 m

Distribution of the nodes random uniform

Number of routes originating at each node

1-10

Route selection shortest path

Number of simulation runs 1000

10.4 Simulation results

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Simulation results

10.4 Simulation results

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Summary

Analytical results:– If everyone drops all packets, it is a Nash-equilibrium– In theory, given some conditions, a cooperative Nash-

equilibrium can exist ( i.e., each forwarder forwards all packets )

Simulation results: – In practice, the conditions for cooperative Nash-equilibria

are very restrictive : the likelihood that the conditions for cooperation hold for every node is extremely small

Consequences:– Cooperation cannot be taken for granted– Mechanisms that stimulate cooperation are necessary

• incentives based on virtual currency• reputation systems

10.5 Summary


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