Incentivizing Sharing in P2P Networks

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

2. 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

4. A query in Napster

5. Free-rider problem • 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 decline to perform this altruistic act

6. 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: σ0(none), σ1(moderate) or σ2(heavy) • Downloading: δ0(none), δ1(moderate) or δ2(heavy)

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

8. Agent Utility Cont. • The equation for agent Ai’s utility function: Ui = [fiAD(AD) + fiNV(NV) + fiAL(AL)] - [fiDS(DS) + fiBW(BW)] –FT

9. Agent Utility Cont. • Two assumptions about agents’ relative preferences for different outcomes: fAD(k) > kβ fDS(k) + fBW(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 (2) The monetary cost to agents of sharing files at level k and uploading them at level k is less than kβ

10. Equilibria • The joint strategies of all agents as ∑ = { S1 … Sn} • 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.

11. Micro-Payment Mechanisms • 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) • C = g(δ- v) • The global sum of all micro-payments is 0 • Individual users may make a profit.

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

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

14. Rewards for Sharing • Penalizing downloads and rewarding agents in proportion to the amount of material they share • An internal currency, “point” • If Ai shares at level s then his expected number of uploads, vi, is :

15. Rewards for Sharing Cont. • ∑ = {(σ2, δ2), … , (σ2,δ2)} is a strict equilibrium • n-1 agents playing the strategy S=(σ2,δ2) • According to fAD(k) > kβ, agent Ai will play S = (σs,δ2) • fDS(k) + fBW(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.

16. Rewards for Sharing Cont. • ∑ = {(σ0, δ2), … , (σ0,δ2)} is a strict equilibrium • n-1 agents playing the strategy S=(σ0,δ2) • Agent Ai will follow strategy S. • Since no files to download • Ai 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

17. Experimental Setup • Extending theoretical model in two ways: • Action spaces for agents more fine-grained • Files of several kinds and agents of several types • Agent utility functions differ as follows: • Altruism: f(AL) =ρAL, ρfrom [ρmin, ρmax] • 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∑ifi(ADi), where each i represents a different kind of file, the factor µ is chosen uniformly at random in [µmin, µmax]

18. 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 use the temporal difference (TD) Q-learning algorithm to learn best response • Assuming the environment does not evolve over time • Q(a,s)  (1–α)Q (a, s) +α(P (a, s) + c*maxa’ Q(a’, s’)) • a is the action that the agent took • s is the current state, s’ is the new state • P(a,s) is the payoff of the current round • The decay 0<α<1 and the future income discount 0<c<1 are fixed

19. Experimental Results

20. Experimental Results Cont.

21. Experimental Results Cont.

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