performance analysis of reputation-based mechanisms for multi-hop wireless networks fabio milan...

Performance Analysis of Reputation-based Mechanisms for Multi-hop Wireless Networks

Fabio MilanDipartimento di Elettronica

Politecnico di TorinoTurin, Italy

Email: [email protected]

Juan José Jaramillo and R. SrikantCoordinated Science Laboratory

Dept. of Electrical and Computer EngineeringUniversity of Illinois at Urbana-Champaign

Email: {jjjarami, rsrikant}@uiuc.edu

March 22, 2006 CISS 2006, Princeton, NJ, USA 2

Outline

• Problem Formulation

• Cooperation without Collisions

• Cooperation with Collisions

• Performance Analysis


Packet Forwarding

A B C

+α –β

• When B forwards a packet for A, node A gains α units and node B loses β units due to energy expenditure


Utility

ui = βpi – αp-i

• α is the packet value• β is the transmission cost

• pi is the dropping probability of node i

• p-i is the dropping probability of the neighbor of node i

• βpi is the gain of dropping packets from the neighbor

• αp-i is the loss for packets being dropped by the neighbor


Utility

• Payoff of mutual cooperation 0

• Payoff of mutual defection β – α

• Packet value is greater than transmission cost

• Mutual cooperation is preferable to mutual defection

1


It’s a Prisoner’s Dilemma

• Each node drops all packets to maximize its utility

• The Nash Equilibrium is

• Individual selfishness leads to zero throughput

• In multi-hop wireless networks, packet relaying requires cooperation

• Need for mechanisms to sustain cooperation among selfish nodes

pi* = p-i

* = 1


Incentives for Cooperation

• Micro-payments

• Reputation-based Mechanisms

– End-to-end

– Hop-by-hop

• With Information Exchange

• Without Information Exchange

– Advantages

» No Control Overhead

» Collusion Resistance

» Full Decentralization

– Disadvantages

» Performance Degradation due to Packet Collisions


Outline






Reputation-based Mechanism

• Nodes take into account the effect of their actions on their future payoff

• The weight of the k-th future payoff is δk

• δ is the discount parameter

0 ≤ δ ≤ 1

• Nodes play a Repeated Game

• δ is the probability to continue to play after each stage


Tit-for-tat

• Cooperate on the first move, then do what the opponent did in the previous move

pi(0) = 0

pi(k) = p-i

(k-1)

k > 0


One-step Deviation

• If both nodes cooperate, their payoff is 0.

• Assume that node i deviates, by setting a dropping probability p>0

– Node i initially benefits from this deviation

– As the neighbor reacts, node i suffers packet losses

– Node i reacts to the punishment by punishing its neighbor

– …

• The discounted payoff of i in case of deviation is a function of α, β, δ and p

• If it is not greater than 0, then being the first to defect is not rational


Equilibrium

• Deviation from Tit-for-tat is not profitable if

1

• If δ is sufficiently large, the outcome is mutual cooperation

• If transmission cost is close to packet value, then cooperation emerges only if the users are farsighted or stay in the system for a very long time


Outline






The Hidden Terminal is Back

B C D E

– α –β

A

• When D forwards a packet from C to E, interference may prevent C to hear this transmission

• C does not know if D is cooperating or not


Perceived Defection

( )( ) ( )p pik

ik 1

• Packet collisions with “hidden terminals” result in a distorted reputation

• Estimate of neighbor’s dropping probability: either cannot “hear” neighbors transmission due to another neighbor’s transmission () or can hear and neighbor drops a relay packet


Queueing Model

λ

Dropped Traffic

∞Generated Traffic

Transit Traffic

• Infinite Backlog, no end-to-end Congestion Control• A node always transmits, within the MAC constraints: either it transmits its own packet or a relay packet

• The network load λ is independent of the dropping probabilities if


Tit-for-tat

p p

ki

kik( ) ( )

1

0

• Cooperate on the first move, then do what you believe the opponent did in the previous move

pi(0) = 0


Retaliation

• Due to collisions, simple Tit-for-tat is not sufficient to sustain cooperation

p

~p

0 1

1

λ

Tit-for-tat

Perceived Defection

• Even if nodes initially cooperate, unjust punishment of perceived defection progressively leads to zero throughput


Generous Tit-for-tat

p

~p

0 1

1

λ


Perceived Defection

• Add a tolerance threshold to mitigate throughput loss

• The optimal tolerance to avoid both retaliation and exploitation is λ



p p

ki

kik( ) ( )m ax{ , }

1 0

0

pi(0) = 0

• Cooperate on the first move, then cooperate more than what you believe the opponent did in the previous move


Equilibrium

11

1 2

( )

• Deviation from Generous Tit-for-tat is not profitable if

• If δ is sufficiently large, the outcome is mutual cooperation

• Need an even larger δ now due to imperfect knowledge of neighbor’s actions


Outline






Game Parameters• λ is a measure of the network load, if every node transmits at the same rate

• δ is a measure of the session length– If a session involves a great number of packets, it is reasonable to assume δ →

1

• α is a measure of the information contained in a packet, with respect to the overall information flow transferred from source to destination

– For a multimedia stream source, tolerant to packet losses, the packet value is small. For a file transfer source, the packet value is high.

• β is a measure of the energy spent to transmit a packet, with respect to the total energy available to the node

– For a terminal connected to the AC power, the transmission cost is low. For a terminal running out of battery, the transmission cost is high.


Throughput Upper Bound

0

Cooperative Nodes

Selfish Nodes

1 1

Throughput

Offered Load

• Beyond this critical threshold, nodes perceive no incentive to cooperate


Packet Value Lower Bound

1

1 2( )

9

4

1

3

1/3 1/3 1/3

• The capacity of a wireless network is limited (Gupta – Kumar, 2000)

• If α is sufficiently large, there exists a value of δ that achieves cooperation for every feasible load

1


Conclusion• Developed a game-theoretic framework to evaluate the performance of hop-

by-hop reputation-based mechanisms for multi-hop wireless network, in presence of packet collisions with “hidden terminals”

• Explored the conditions for the emergence of cooperation in a network of selfish users, in terms of network load, session length, application type and energy constraints

• Ongoing work: How does the network topology affects the conditions for the emergence of cooperation?

• Ongoing work: Simulation experiments to study how the externalities introduced by an end-to-end congestion control affect the stability of the mechanism

• As for now, our model suggests that if nodes use Skype™ while running out of battery, then they are unlikely to cooperate…


Thank You!

performance analysis of reputation-based mechanisms for multi-hop wireless networks fabio milan...

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