chapter 10: selfishness in packet forwarding
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© 2007 Levente Buttyán and Jean-Pierre Hubaux
Security and Cooperation in Wireless Networks
http://secowinet.epfl.ch/
Chapter 10: Selfishness in packet forwarding
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?
3/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
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
4/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
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
5/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
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
6/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
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
7/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
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
8/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
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
9/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
Concept of dependency graph
dependency: the benefit of each source is dependent on the behavior of its forwarders
dependency loop
10.2 Meta-model
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
11/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
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
12/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
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
13/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
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
14/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
Simulation results
10.4 Simulation results
15/15Security and Cooperation in Wireless NetworksChapter 10: Selfishness in packet forwarding
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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