Incentives for Sharing in Peer-to-Peer Networks By Philippe Golle, Kevin Leyton-Brown, Ilya Mironov, Mark Lillibridge

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

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Free-rider problem The phenomenon of selfish individuals who opt out of a voluntary contribution to a group ’ s common welfare The phenomenon of selfish individuals who opt out of a voluntary contribution to a group ’ s common welfare Users do not benefit from serving files to others Users do not benefit from serving files to others Users decline to perform this altruistic act

Problem 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: σ 0(none), σ 1(moderate) or σ 2(heavy) Downloading: δ0(none), δ1(moderate) or δ2(heavy)

Agent Utility Amount Downloaded (AD): Agents get happier the Amount Downloaded (AD): Agents get happier the more they download more they download Network Variety (NV): Agents prefer to have more Network Variety (NV): Agents prefer to have more options options Altruism (AL): Satisfaction of contributing to the network Altruism (AL): Satisfaction of contributing to the network Disk Space Used (DS): A cost of allocating disk space to Disk Space Used (DS): A cost of allocating disk space to sbe used sbe used Bandwidth Used (BW): A cost of uploading files to Bandwidth Used (BW): A cost of uploading files to network network Financial Transfer (FT): Agents may ends up paying Financial Transfer (FT): Agents may ends up paying money or getting paid for usage money or getting paid for usage of the network of the network

Agent Utility Cont. The equation for agent Ai ’ s utility function: The equation for agent Ai ’ s utility function: U i = [f i AD (AD) + f i NV (NV) + f i AL (AL)] U i = [f i AD (AD) + f i NV (NV) + f i AL (AL)] - [f i DS (DS) + f i BW (BW)] –FT - [f i DS (DS) + f i BW (BW)] –FT

Agent Utility Cont. Two assumptions about agents ’ relative preferences for different outcomes: Two assumptions about agents ’ relative preferences for different outcomes: f AD (k) > kβ f AD (k) > kβ f DS (k) + f BW (k) < kβ f DS (k) + f BW (k) < kβ (1) The monetary equivalent of the utility agents gain from downloading files at level k is more than kβ, for some constant β (1) The monetary equivalent of the utility agents gain from downloading files at level k is more than kβ, for some constant β (2) The monetary cost to agents of sharing files at level k and uploading them at level k is less than kβ (2) The monetary cost to agents of sharing files at level k and uploading them at level k is less than kβ

Equilibria The joint strategies of all agents as The joint strategies of all agents as ∑ = { S 1 … S n } ∑ = { S 1 … S n } Weak Nash equilibrium: when no agent can gain by changing 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 Mechanisms To charge users for every download and to reward then for every upload. To charge users for every download and to reward then for every upload. The server tracks the number of files downloaded (δ) and uploaded (v) The server tracks the number of files downloaded (δ) and uploaded (v) C = g(δ- v) C = g(δ- v) The global sum of all micro-payments is 0 The global sum of all micro-payments is 0 Individual users may make a profit. Individual users may make a profit.

Micro-Payment Mechanisms Cont. If agent Ai chooses the action (σ s,δ d ), its expected payment to the system: If agent Ai chooses the action (σ s,δ d ), its expected payment to the system: β: the cost/reward per fileβ: the cost/reward per file σ -i be the total number of units shared by agents otherσ -i be the total number of units shared by agents other than Ai than Ai δ -i be the total number of units downloaded by agents otherδ -i be the total number of units downloaded by agents other than Ai. than Ai.

Quantized Micro-Payment Mechanisms Users pay for downloads in blocks of b files, where b is a fixed parameter. Users pay for downloads in blocks of b files, where b is a fixed parameter. Advantage: agents are spared the mental decision costs associated with per-download pricing Advantage: agents are spared the mental decision costs associated with per-download pricing Property: after one file has been downloaded, the marginal cost of downloading the remaining b-1 files belongs to the same block is zero. Property: after one file has been downloaded, the marginal cost of downloading the remaining b-1 files belongs to the same block is zero.

Rewards for Sharing Penalizing downloads and rewarding agents in proportion to the amount of material they share Penalizing downloads and rewarding agents in proportion to 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, v i, is : If Ai shares at level s then his expected number of uploads, v i, is :

Rewards for Sharing Cont. ∑ = {(σ 2, δ 2 ), …, (σ 2,δ 2 )} is a strict equilibrium ∑ = {(σ 2, δ 2 ), …, (σ 2,δ 2 )} is a strict equilibrium n-1 agents playing the strategy S=(σ 2,δ 2 )n-1 agents playing the strategy S=(σ 2,δ 2 ) According to f AD (k) > kβ, agent Ai will play S = (σ s,δ 2 )According to f AD (k) > kβ, agent Ai will play S = (σ s,δ 2 ) f DS (k) + f BW (k) < kβ, tells us that agents prefer to share at level k and upload at level k than to pay the system for k points.f DS (k) + f BW (k) < kβ, tells us that agents prefer to share at level k and upload at level k than to pay the system for k points.

Rewards for Sharing Cont. ∑ = {(σ 0, δ 2 ), …, (σ 0,δ 2 )} is a strict equilibrium ∑ = {(σ 0, δ 2 ), …, (σ 0,δ 2 )} is a strict equilibrium n-1 agents playing the strategy S=(σ 0,δ 2 )n-1 agents playing the strategy S=(σ 0,δ 2 ) 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 requests, bringing him negative utilityAi will be made to serve files for all other agents’ download requests, bringing him negative utility Offering distributors different rewards based on expected download demand Offering distributors different rewards based on expected download demand

Experimental 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) =ρAL, ρ from [ρ min, ρ max ]Altruism: f(AL) =ρAL, ρ from [ρ min, ρ max ] Disk Space: f(DS) is set to emulate an agent with maximal storage space d, d from [d min, d max ]Disk Space: f(DS) is set to emulate an agent with maximal storage space d, d from [d min, d max ] File type preference: the term f(AD) is decomposed into µ∑ i f i (AD i ), where each i represents a different kind of file, the factor µ is chosen uniformly at random in [µ min, µ max ]File type preference: the term f(AD) is decomposed into µ∑ i f i (AD i ), where each i represents a different kind of file, the factor µ is chosen uniformly at random in [µ min, µ max ]

Learning Algorithm Agents behave as if other agents ’ strategies were fixed, and make a best response based on their observations of other agents ’ actions Agents behave as if other agents ’ strategies were fixed, and make a best response based on their observations of other agents ’ actions Agents use the temporal difference (TD) Q-learning algorithm to learn best response Agents use the temporal difference (TD) Q-learning algorithm to learn best response Assuming the environment does not evolve over time Assuming the environment does not evolve over time Q(a,s)  (1 – α)Q (a, s) Q(a,s)  (1 – α)Q (a, s) +α(P (a, s) + c*max a’ Q(a’, s’)) +α(P (a, s) + c*max a’ 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<α<1 and the future income discount 0<c<1 are fixedThe decay 0<α<1 and the future income discount 0<c<1 are fixed

Experimental Results

Experimental Results Cont.

Conclusion Free-rider problem is a real issue for P2P systems Free-rider problem is a real issue for P2P systems Free-rider become even more important in commercial systems Free-rider become even more important in commercial systems A simple game theoretic model of agent behavior is proposed A simple game theoretic model of agent behavior is proposed