DARWIN: Distributed and Adaptive Reputation Mechanism for Wireless Ad-hoc NetworksCHEN Xiao Wei, Cheung Siu Ming

CSE, CUHKMay 15, 2008

This talk is based on paper: Juan José Jaramillo and R. Srikant. DARWIN: Distributed and Adaptive Reputation Mechanism for Wireless Ad-hoc Networks. In Proc. of ACM 13th Annual International Conference on Mobile and Networking (MobiCom’07), Montreal, Canada, Sept. 2007

Outline Introduction Basic Game Theory Concepts Network Model Analysis of Prior Proposals

Trigger Strategies Tit For Tat Generous Tit For Tat

DARWIN Contrite Tit For Tat Definition Performance Guarantees Collusion Resistance Algorithm Implementation

Simulations Settings Results

Conclusion & Comments

Introduction

Source communicates with distant destinations using intermediate nodes as relays

Cooperation: Nodes help relay packets for each other

In wireless networks, nodes can be selfish users that want to maximize their own welfare.

Incentive mechanisms are needed to enforce cooperation.

Introduction (Cont.)

Two types of incentive mechanisms:Credit exchange systems: by paymentReputation based systems: by neighbor's

observation

Introduction (Cont.)

Main issue Due to packet collisions and interference, sometimes

cooperative nodes will be perceived as being selfish, which will trigger a retaliation situation

Contributions Analyze prior reputation strategies’ robustness Propose a new reputation strategy (DARWIN) and

prove its robustness, collusion resistance and cooperation.

The Prisoners’ Dilemma Game

A Nash equilibrium is a strategy profile having the property that no player can benefit by unilaterally deviating from its strategy

Repeated Prisoner’s Dilemma Game Total payoff function is the discounted sum of the stage

payoffs:

( )

0

k ki i

k

U w u

Network Model

Assumptions Nodes are selfish and rational, not malicious Node operate in promiscuous mode The value of a packet should be at least equal to the cost of the

resources used to send it. (α≥1) Assume any two neighbors have uniform network traffic

demands. Thus, two player’s game. Other Assumptions

Two nodes simultaneously decide whether to drop or forward their respective packets, and repeat game iteratively

Game time is divided into slots

Payoff Matrix

Affine Transformation

Payoff Matrix (Cont.)

Define pe (0,1) to be the probability of a packet that has ∈been forwarded was not overheard by the originating node.

Define to be the perceived dropping probability of node i’s neighbor at time slot k≥0 estimated by node i.

( )ˆ kip

( ) ( ) ( ) ( )ˆ (1 ) (1 )k k k ki i i e e e ip p p p p p p

is the average payoff at time slot k

Payoff Function

( )kiu

Average discount average payoff of player i starting from time slot n is then given by

( )niu

( ) ( )n k n ki i

k n

U w u

N-step Trigger Strategy

If node i’s neighbor cooperates, then and then the optimal value of T=pe

Actually, pe is hard to perfectly estimated, so we have two cases: If T<pe, cooperation will never emerge.

If T>pe, player –i will be perceived to be cooperative as long as it drops packets with probability

Full Cooperation is never the NE point with trigger strategies

Trigger Strategies

( )ˆ ki ep p

( )

1k ei

e

T pp

p

Define to be the dropping probability node i should use at time slot k according to strategy S.

( )S

kip

Tit For Tat

Tit For Tat Strategy

Milan et al. proved that TFT does not provide the right incentive either for cooperation in wireless networks.

Generous Tit For Tat

Use a generosity factor g that allows cooperation to be restored. GTFT strategy

GTFT is a robust strategy where no node can gain by deviating from the expected behavior, even if it cannot achieve full cooperation.

But according to the Corollary:

If both nodes use GTFT the cooperation is achieved on the equilibrium path if and only if g=pe

So GTFT also needs a perfect estimate of pe

DARWIN

GOAL: propose a reputation strategy that does not depend on a perfect estimation of pe to achieve full cooperation

FOUNDATION: “Contrite Tit For Tat” strategy in iterated Prisoners’ Dilemma

Contrite Tit For Tat

Base on idea of contriteness Player always in good standing on first stage Player should cooperate if it is in bad

standing, or if its opponent is in good standing

Otherwise, the player should defect

DARWIN

1

-1

Note: Use historic information, e.g. qi

(k-1)

qi(k) acts as a measurement of bad standing

Can you find the “Contrite Tit F

or Tat” idea?

Performance Guarantees

Theorem: Assume 1<γ<pe-1, DARWIN is su

bgame perfect if and only if

The problem: The exact value of pe is not known, so how do we decide γ?

Based on estimated pe:

Performance Guarantees

Estimated error probability: pe

(e) = pe + Δ where –pe<Δ<1-pe

Substitute into previous equation:

For the assumption to be true (1<γ<pe-1)

Precise estimate of pe is not required

Δ < 1 - pe

Performance Guarantees

LEMMA: If both nodes use DARWIN then cooperation is achieved on the equilibrium path. That is,

pi(k) = p-i

(k) = 0 for all k>=0

Collusion Resistance

Define to be the discounted average payoff of player i using strategy Si when it plays against player –i using strategy S-i

Define ps (0,1) to be the probability that a ∈node that implements DARWIN interacts with a colluding node.

(0)|i ii S SU

Collusion Resistance (Cont.)

Then we can get the average payoff to a cooperative node

Similarly, the average payoff to a colluding node interacts with a node implementing DARWIN

(0) (0)| |( ) (1 )i D S i D DU D psU ps U

(0) (0)| |( ) (1 )i S D i S SD DU S p U p U

Collusion Resistance (Cont.)

The average payoff is bounded by

A group of colluding nodes cannot gain from unilaterally deviating if and only if

U(S) ＜ U(D), that is

Collusion Resistance (Cont.)

Define strategy S to be a sucker strategy if

(0) (0)| |i D D i D SU U

denotes connectivity, which is the forwarding ratio

Algorithm Implementation

( )( )

( )

kijk

ij kij

Fc

S

( )kijF

( )kijS The number of messages sent to j for forwarding

The number of messages j actually forwarded

( )kijc

Then j’s average connectivity ratio is

( )

( )

( ) ( )

{ }( )

( )

{ }

ˆkim j

kim j

k kim mj

m N ikj k

imm N i

c c

cc

Algorithm Implementation (Cont.) Define Use equation (6) and (7) to find the

dropping probability To meet

We estimate pe as , which is the fraction of time at least one node different from j transmits

( ) ( )ˆ ˆ1k kj jp c

1ep

ˆejp

Simulations

Settingsns-2Dynamic Source Routing (DSR) ProtocolArea: 670 x 670m2

50 nodes randomly placed, some are selfish14 source-destination pairspacket size is 512 byteSimulation time is 800s, time slot is 60sγ=2

Simulations

Normalized forwarding ratio Fraction of forwarded packets in the network under

consideration divided by fraction of forwarded packets in a network with no selfish nodes

Objective Find how normalized forwarding ratios for both cooperative

and selfish nodes vary with: Dropping probability of selfish nodes Source rate Percentage of selfish nodes

Simulations

Normalized forwarding ratio for different dropping ratio of selfish nodes

5 selfish nodes

2 packets/s

Simulations

Normalized forwarding ratio for different source rates

5 selfish nodes

100% dropping ratio for selfish nodes

Simulations

Normalized forwarding ratio for different number of selfish nodes

2 packets/s

100% dropping ratio for selfish nodes

Key pt.: Selfishness does not improve performance

Nodes are rational

Conclusion

Studied how reputation-based mechanisms help cooperation emerge among selfish users Showed properties of previously proposed schemes Proposed new mechanism called DARWIN

DARWIN is Robust to imperfect measurements (pe) Collusion-resistant Able to achieve full cooperation (LEMMA) Insensitive to parameter choices

Comments

Contribution: Apply CTFT to Wireless Ad-hoc Networks

Reliable as long as assumptions hold Assumed nodes do not lie about perceived dropping

probability Liars can get better payoffs!

Assumed nodes are rational Only the previous stage is considered Normalized forward rates, but not payoff, is shown in

simulation results.

Thanks