A Game Theoretic Approach to Provide Incentive and Service Differentiation in P2P Networks Richard Ma, Sam Lee, John Lui (CUHK) David Yau (Purdue)

Outline Problem, Issues & System Infrastructure Resource Distribution Mechanisms Resource Competition Games Experiments & Conclusions

Problems P2P information exchange paradigm Free-riding problem –Nearly 70% users do not share. Tragedy of the Commons –Nearly 50% request responses are from top 1% nodes. Objective –Provide Incentive to share information. –Provide Service Differentiation for users.

Issues How to provide incentives for users? –Contribution measure. –Differentiated services. How to distribute bandwidth resource? –Various physical types & contributions. –Fairness and efficiency concern. How to adapt to network dynamics? –Join and leave. –Network congestion.

System Infrastructure: Terms Contribution value C i Bidding value b i Allocated bandwidth x i Actual receiving bandwidth x i ’ node i

System Infrastructure: Interactions time bi(t0)bi(t0) xi(t0)xi(t0) xi(t1)xi(t1) (b i,C i ) (b j,C j ) (b k,C k ).. bi(t1)bi(t1) competing node i source node s xi’(t1)xi’(t1) xi’(t0)xi’(t0) WsWs

Resource Distribution Mechanisms (source node side) Objectives –Design an resource distribution function: f : {C i }×{b i } → {x i }. –Design an algorithm to achieve the function. Desired Properties and Constraints –Non-negative constraint on bandwidth: x i ¸ 0. –Budget constraint on total bandwidth:  x i · W s. –Desirability constraint on bandwidth: x i · b i. –Pareto optimality:  b i ¸ W s !  x i = W s otherwise x i = b i 8 i.

Resource Distribution Mechanisms (an example) Three competing nodes. Bidding values: – b 1 = 2 Mbps, b 2 = 5 Mbps, b 3 = 8 Mbps. Source node’s bandwidth capacity: –W s = 10 Mbps.

Non-negative constraint Budget constraint Desirability constraint Pareto optimality W s = 10; (b 1,b 2,b 3 ) = (2,5,8)

Resource Distribution Mechanisms: Base-line algorithm Progressive filling algorithm Pareto optimal Solving the problem: –Maximize  x i –Subject to  x i · W s 0 · x i · b i 8 i Max-min fairness W s = 10; (b 1,b 2,b 3 ) = (2,5,8) (x 1,x 2,x 3 ) = (2,4,4)

Resource Distribution Mechanisms: Incentive-based Contribution weighted filling Pareto optimal Solving the problem: –Maximize  C i x i –Subject to  x i · W s 0 · x i · b i 8 i Proportional to contribution values (C 1,C 2,C 3 ) = (2,5,3) (x 1,x 2,x 3 ) = (2,5,3) W s = 10; (b 1,b 2,b 3 ) = (2,5,8)

Resource Distribution Mechanisms : Utility concerns –Utility concern for nodes. –Denote U i (x i,b i ) as the utility function, indicating the degree of happiness of node i. –Our utility function: U i (x i,b i )= log(x i /b i +1). –Concavity, Through origin, Same maximum utility.

Resource Distribution Mechanisms: Incentive and Utility Marginal utility weighted by contribution: C i U i ’ = C i /(x i + b i ) Pareto optimal Solving the problem: –Maximize  C i U i –Subject to  x i · W s 0 · x i · b i 8 i Linear time complexity W s = 10; (b 1,b 2,b 3 ) = (2,5,8); U i = log (x i / b i +1) (C 1,C 2,C 3 ) = (2,5,3) (x 1,x 2,x 3 ) = (2,5,3)

Resource Competition Games Consider the competing node’s side: What is the optimal value of b i for node i ? time bi(t0)bi(t0) xi (t0)xi (t0) competing node i source node s (b i,C i ) (b j,C j ) (b k,C k ).. WsWs U=log(x/b+1) ! (x i,x j,x k..)

Resource Competition Games -- the theoretical game General gameResource competition game –PlayersCompeting nodes –StrategiesBidding values –Game rulesResource distribution mechanism –OutcomeBandwidth allocated to nodes Achieved game properties –Pareto optimality –Unique Nash equilibrium –Contribution proportional solution in equilibrium –Collusion proof

Resource Competition Games -- the Nash equilibrium The Nash equilibrium (b *, x * ) b i * = x i * = (C i /  C j ) W s 8 i Nash strategy for the previous example: b 1 * =2, b 2 * =5, b 3 * =3. Verifications : –When b i * is decreased to be b i, by the desirability constraint, x i is at most b i. –When b i * is increased to be b i, x i does not increase.

Practical game issues Common knowledge problem –How to bring the nodes to the Nash equilibrium? Wastage problem –Node may have a maximal download bandwidth, which is less than what it can receive in the Nash equilibrium. Network dynamics problem –Arrival and departure. –Network congestion.

Any new arrival or departure leads to a new equilibrium. W s = 2 (Mbps) Contribution: [ 400, 300, 200, 100 ] Maximal receiving bandwidth: [ 2, 1.5, 1, 0.5 ] (Mbps) Arrival time: [ 20, 80, 60, 40 ] Departure time: [ 100, 120, 140, 160 ] Proportional share in equilibrium. No bandwidth wastage.

Equilibrium change due to the congestion. Proportional sharing among un-congested nodes. W s = 2 (Mbps) Contribution: [ 400, 300, 200, 100 ] Maximal receiving bandwidth: [ 2, 1.5, 1, 0.5 ] (Mbps) Congestion period for node 1: [ 20, 30 ] & [ 60, 70 ] and has a maximal receiving bandwidth 0.4 Mbps

Conclusions Service differentiations –Contribution, utility and fairness concerns –Linear-time algorithm for resource allocation Equilibrium solution –Pareto optimal (global efficiency) –Nash solution (selfish and rational) –Proportional to contribution (incentive) –Collusion proof (secure and rational) Adaptive to network dynamics –Dynamic join/leave –Network congestion

Questions and Answers