A Game Theoretic Framework for Incentives in P2P Systems --- CS. Uni. California

1. A Game Theoretic Framework for Incentives in P2P Systems--- CS. Uni. California Jun Cai Advisor: Jens Graupmann

2. Outline • Introduction (problem, motivation) • Incentive model • Nash Equilibrium in Homogeneous Systems of Peers • Nash Equilibrium in Heterogeneous Systems of Peers • Simulation result • Summary

3. Introduction Democratic nature, no central authority mandate resource Distributed resources are highly variable and unpredictable Most of users are “free riders” (In Gnutella, 25% users share nothing) User session are relative short, 50% of sessions are shorter than 1 hour

4. How to build a reliable P2P system • Require: Contribution should be predictable • Peers can be motivated using economic principle • Monetary payment (one pays to consume resources and paid to contribute resource) • Differential service (peers that contributes more get better quality of service) eg: reputation index (participation level in KaZaA) KaZaA: Participation level = upload in MB / download in MB x 100

5. Modeling interaction of peers by Game Theory • Peers are strategic and rational player • Non-cooperative game • Each player wants to maximize his utility • Utility depends on benefit and cost • Utility depends not only on his own strategy but everybody else’s strategy • Find equilibrium (a locally optimum set of strategies) where no peer can improve his utility --- Nash equilibrium Level of contribution Uptime or shared disk space, bandwidth

6. Incentive model (measure contribution) • P1,P2,P3…PN as peers • Utility function for Pi is Ui • Contribution of Pi is Di(D0 is absolute measure of contribution) • Dimensionless contribution: • Unit cost ci • Total cost:ciDi

7. Incentive model (Benefit matrix) • NxN benefit matrix B • Bij denote how much the contribution made by Pj is worth to Pi • bi is the total benefit that Pi can get from the system There exists a critical value bc.

8. Incentive model (A peer reward other peers in proportion to their contribution) • Pj accepts a request for a file from peer Pi with probability p(di) and rejects it with probability 1-p(di) • Each request is tagged with di as metadata

9. Incentive model (Utility function) • Utility function • Dimensionless utility function Be able to download? benefit cost worth

10. Utility vs. contribution (different benefit)

11. So far… • Incentive model • Now find equilibrium… • Homogeneous (simple) • Heterogeneous (by analogy of Homogeneous system)

12. Homogeneous System of Peers (1) • All peers derive equal benefit form everybody else (bij=b for ) • By symmetry, reduce the problem to Two player game • Best response function P1: P2: Differentiate w.r.t. d1 Differentiate w.r.t. d2

13. Nash Equilibrium in Homogeneous System of Peers (2) • Best response function • Nash equilibrium exists if forms a fix point for above equation Solution exists only if Utility contribution

14. Critical benefit value bc b=bc

15. Nash Equilibrium in Homogeneous System of Peers (3) • N player game Replace b(N-1) to b, this formula is two player game.

16. Courtnot learning & convergence process High Low

17. Nash Equilibrium in Heterogeneous System • In Homogeneous system, fix point equation: • In Heterogeneous system, fix point equation: By analogy of Homogeneous system

18. Iterative learning model Algorithms: iterative learning model di = random contribution While (converge == false){ new_di = computeContribution (d, b); if (new_di == di) { converge = true; } di = new_di; }

19. Convergence of learning algorithms High benefit How fast it converge? Low benefit

20. Simulation: dav vs. (bav/bc-1) Equilibrium average contribution 1. Monotonically 2. Peer size independent 3. If bav < bc, d ---> 0

21. Simulation: leave system bav/bc-1=2.0

22. Summary • Differential service based incentive model for p2p system that eliminating free riding and increasing availability of the system • Critical benefit bc