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

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

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

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

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

Incentive model (measure contribution) P 1,P 2,P 3 …P N as peers Utility function for P i is U i Contribution of P i is D i (D 0 is absolute measure of contribution) Dimensionless contribution: Unit cost c i Total cost:c i D i

Incentive model (Benefit matrix) NxN benefit matrix B B ij denote how much the contribution made by P j is worth to P i b i is the total benefit that P i can get from the system There exists a critical value b c.

Incentive model (A peer reward other peers in proportion to their contribution) P j accepts a request for a file from peer P i with probability p(d i ) and rejects it with probability 1-p(d i ) Each request is tagged with d i as metadata

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

Utility vs. contribution (different benefit)

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

Homogeneous System of Peers (1) All peers derive equal benefit form everybody else (b ij =b for ) By symmetry, reduce the problem to Two player game Best response function Differentiate w.r.t. d 1 Differentiate w.r.t. d 2 P1: P2:

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

Critical benefit value b c b=b c

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

Courtnot learning & convergence process High Low

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

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; }

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

Simulation: d av vs. (b av /b c -1) Equilibrium average contribution 1. Monotonically 2. Peer size independent 3. If b av 0

Simulation: leave system b av /b c -1=2.0

Summary Differential service based incentive model for p2p system that eliminating free riding and increasing availability of the system Critical benefit b c