Incentives for Sharing in Peer-to-Peer Networks

By Philippe Golle, Kevin Leyton-Brown,

Ilya Mironov, Mark Lillibridge

What is P2P What is P2P

In a Peer-to-Peer network, end users share resources via direct exchange between computers

Information is distributed among the member nodes instead of concentrated at a single server

A pure peer to peer system is a distributed system without any centralized control, where the software running at each node is equivalent in functionality

A query in NapsterA query in Napster

Free-rider problem Free-rider problem

The phenomenon of selfish individuals who opt The phenomenon of selfish individuals who opt out of a voluntary contribution to a group’s out of a voluntary contribution to a group’s common welfarecommon welfare

Users do not benefit from serving files to othersUsers do not benefit from serving files to others

Users decline to perform this altruistic act

Problem DefinitionProblem Definition

we describe the game that we use to model the file sharing scenario during one time period

• n agents participate in the system: A1, . . . , An.• Each agent Ai’s strategy: Si = (σ,δ)

Sharing: σ0(none), σ1(moderate) or σ2(heavy) Downloading: δ0(none), δ1(moderate) or δ2(heavy)

Agent UtilityAgent Utility Amount Downloaded (AD):Amount Downloaded (AD): Agents get happier the Agents get happier the more they downloadmore they download Network Variety (NV):Network Variety (NV): Agents prefer to have more Agents prefer to have more optionsoptions Altruism (AL):Altruism (AL): Satisfaction of contributing to the network Satisfaction of contributing to the network

Disk Space Used (DS):Disk Space Used (DS): A cost of allocating disk space to A cost of allocating disk space to sbe usedsbe used Bandwidth Used (BW):Bandwidth Used (BW): A cost of uploading files to A cost of uploading files to networknetwork Financial Transfer (FT):Financial Transfer (FT): Agents may ends up paying Agents may ends up paying money or getting paid for usage money or getting paid for usage of the networkof the network

Agent Utility Cont.Agent Utility Cont.

The equation for agent Ai’s utility function:The equation for agent Ai’s utility function:

UUi i = [f= [fiiADAD(AD) + f(AD) + fii

NVNV(NV) + f(NV) + fiiALAL(AL)](AL)]

- [f- [fiiDSDS(DS) + f(DS) + fii

BWBW(BW)] –FT(BW)] –FT

Agent Utility Cont.Agent Utility Cont.

Two assumptions about agents’ relative preferences Two assumptions about agents’ relative preferences for different outcomes:for different outcomes:

ffADAD(k) > k(k) > kββ

ffDSDS(k) + f(k) + fBWBW(k) < k(k) < kββ

(1) The monetary equivalent of the utility agents gain from downloading f(1) The monetary equivalent of the utility agents gain from downloading f

iles at level k is more than kiles at level k is more than kββ, for some constant , for some constant ββ (2) The monetary cost to agents of sharing files at level k and uploading t(2) The monetary cost to agents of sharing files at level k and uploading t

hem at level k is less than khem at level k is less than kββ

EquilibriaEquilibria

The joint strategies of all agents asThe joint strategies of all agents as ∑ ∑ = { S= { S11 … S … Snn}} Weak Nash equilibrium: when no agent can gain by ch

anging his strategy, given that all other agents’ strategies are fixed.

Strict Nash equilibrium: when every agent would be strictly worse off if he were to change his strategy, given that all other agents’ strategies are fixed.

Dominant Strategy: if his best action does not depend on the action of any other agent.

Micro-Payment MechanismsMicro-Payment Mechanisms

To charge users for every download and to reward theTo charge users for every download and to reward then for every upload.n for every upload.

The server tracks the number of files downloaded (The server tracks the number of files downloaded (δδ) ) and uploaded (v)and uploaded (v)

C = g(C = g(δδ- v)- v) The global sum of all micro-payments is 0The global sum of all micro-payments is 0 Individual users may make a profit.Individual users may make a profit.

Micro-Payment Mechanisms Cont.Micro-Payment Mechanisms Cont.

If agent Ai chooses the action (If agent Ai chooses the action (σσss,,δδdd), its expected payment to the ), its expected payment to the system:system:

• ββ: the cost/reward per file: the cost/reward per file• σσ -i-i be the total number of units shared by agents other be the total number of units shared by agents other than Aithan Ai• δδ-i-i be the total number of units downloaded by agents other be the total number of units downloaded by agents other than Ai.than Ai.

Quantized Micro-Payment MechanismsQuantized Micro-Payment Mechanisms

Users pay for downloads in blocks of b files, Users pay for downloads in blocks of b files, where b is a fixed parameter.where b is a fixed parameter.

Advantage: agents are spared the mental Advantage: agents are spared the mental decision costs associated with per-download decision costs associated with per-download pricingpricing

Property: after one file has been downloaded, the Property: after one file has been downloaded, the marginal cost of downloading the remaining b-1 marginal cost of downloading the remaining b-1 files belongs to the same block is zero.files belongs to the same block is zero.

Rewards for SharingRewards for Sharing Penalizing downloads and rewarding agents in proportion to Penalizing downloads and rewarding agents in proportion to

the amount of material they share the amount of material they share

An internal currency, “point”An internal currency, “point”

If Ai shares at level s then his expected number of uploads, vIf Ai shares at level s then his expected number of uploads, v ii, , is : is :

Rewards for Sharing Cont.Rewards for Sharing Cont.

∑ ∑ = {(= {(σσ22, , δδ22), … , (), … , (σσ22,,δδ22)} is a strict equilibrium )} is a strict equilibrium • n-1 agents playing the strategy S=(n-1 agents playing the strategy S=(σσ22,,δδ22))• According to fAccording to fADAD(k) > k(k) > kββ, agent Ai will play S = (, agent Ai will play S = (σσss,,δδ22))• ffDSDS(k) + f(k) + fBWBW(k) < k(k) < kββ, tells us that agents prefer to share at level k , tells us that agents prefer to share at level k

and upload at level k than to pay the system for k points.and upload at level k than to pay the system for k points.

Rewards for Sharing Cont.Rewards for Sharing Cont.

∑ ∑ = {(= {(σσ00, , δδ22), … , (), … , (σσ00,,δδ22)} is a strict equilibrium)} is a strict equilibrium• n-1 agents playing the strategy S=(n-1 agents playing the strategy S=(σσ00,,δδ22))• Agent Ai will follow strategy S.Agent Ai will follow strategy S.• Since no files to downloadSince no files to download• Ai will be made to serve files for all other agents’ download rAi will be made to serve files for all other agents’ download r

equests, bringing him negative utilityequests, bringing him negative utility Offering distributors different rewards based on expecOffering distributors different rewards based on expec

ted download demandted download demand

Experimental SetupExperimental Setup

Extending theoretical model in two ways:Extending theoretical model in two ways:• Action spaces for agents more fine-grainedAction spaces for agents more fine-grained• Files of several kinds and agents of several typesFiles of several kinds and agents of several types

Agent utility functions differ as follows:Agent utility functions differ as follows:• Altruism: f(AL) =Altruism: f(AL) =ρρAL, AL, ρρ from [from [ρρminmin, , ρρmaxmax]]• Disk Space: f(DS) is set to emulate an agent with maximal storDisk Space: f(DS) is set to emulate an agent with maximal stor

age space d, d from [d age space d, d from [d min min , d , d maxmax]]• File type preference: the term f(AD) is decomposed into µ∑File type preference: the term f(AD) is decomposed into µ∑ iiffii

(AD(ADii), where each i represents a different kind of file, the facto), where each i represents a different kind of file, the factor µ is chosen uniformly at random in [µr µ is chosen uniformly at random in [µminmin, µ, µmaxmax]]

Learning AlgorithmLearning Algorithm Agents behave as if other agents’ strategies were fixed, and maAgents behave as if other agents’ strategies were fixed, and ma

ke a best response based on their observations of other agents’ ke a best response based on their observations of other agents’ actionsactions

Agents use the temporal difference (TD) Q-learning algorithm to lAgents use the temporal difference (TD) Q-learning algorithm to learn best responseearn best response

Assuming the environment does not evolve over timeAssuming the environment does not evolve over time Q(a,s) Q(a,s) (1– (1–αα)Q (a, s))Q (a, s) ++αα(P (a, s) + c*max(P (a, s) + c*maxa’ a’ Q(a’, s’))Q(a’, s’))

• a is the action that the agent tooka is the action that the agent took• s is the current state, s’ is the new states is the current state, s’ is the new state• P(a,s) is the payoff of the current roundP(a,s) is the payoff of the current round• The decay 0<The decay 0<αα<1 and the future income discount 0<c<1 are fixed<1 and the future income discount 0<c<1 are fixed

Experimental ResultsExperimental Results

Experimental Results Cont.Experimental Results Cont.

Experimental Results Cont.Experimental Results Cont.

ConclusionConclusion

Free-rider problem is a real issue for P2P Free-rider problem is a real issue for P2P systemssystems

Free-rider become even more important in Free-rider become even more important in commercial systemscommercial systems

A simple game theoretic model of agent A simple game theoretic model of agent behavior is proposedbehavior is proposed