A Game Theoretic Approach to Provide Incentive and Service Differentiation in P2P Networks

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

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

3. 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.

4. 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.

5. System Infrastructure: Terms • Contribution value Ci • Bidding value bi • Allocated bandwidth xi • Actual receiving bandwidth xi’ node i

6. System Infrastructure: Interactions (bi,Ci) bi(t0) (bj,Cj) (bk,Ck) .. xi(t0) Ws xi’(t0) bi(t1) competing node i source node s xi(t1) time xi’(t1)

7. Resource Distribution Mechanisms (source node side) • Objectives • Design an resource distribution function: f :{Ci}×{bi}→{xi} . • Design an algorithm to achieve the function . • Desired Properties and Constraints • Non-negative constraint on bandwidth:xi¸ 0. • Budget constraint on total bandwidth: xi· Ws. • Desirability constraint on bandwidth: xi· bi. • Pareto optimality:  bi¸ Ws! xi= Wsotherwise xi = bi8 i.

8. Resource Distribution Mechanisms (an example) • Three competing nodes. • Bidding values: • b1 = 2 Mbps, b2 = 5 Mbps, b3 = 8 Mbps. • Source node’s bandwidth capacity: • Ws = 10 Mbps.

9. Non-negative constraint • Budget constraint • Desirability constraint • Pareto optimality Ws = 10; (b1,b2,b3) = (2,5,8)

10. Resource Distribution Mechanisms: Base-line algorithm • Progressive filling algorithm • Pareto optimal • Solving the problem: • Maximize  xi • Subject to •  xi · Ws • 0 · xi· bi8 i • Max-min fairness Ws = 10; (b1,b2,b3) = (2,5,8) (x1,x2,x3) = (2,4,4)

12. Resource Distribution Mechanisms: Incentive-based • Contribution weighted filling • Pareto optimal • Solving the problem: • Maximize  Cixi • Subject to •  xi · Ws • 0 · xi· bi8 i • Proportional to contribution values Ws = 10; (b1,b2,b3) = (2,5,8) (C1,C2,C3) = (2,5,3) (x1,x2,x3) = (2,5,3)

14. Resource Distribution Mechanisms : Utility concerns • Utility concern for nodes. • DenoteUi(xi,bi) as the utility function, indicating the degree of happiness of node i. • Our utility function:Ui(xi,bi)= log(xi/bi+1). • Concavity, Through origin, Same maximum utility.

15. Resource Distribution Mechanisms: Incentive and Utility Ws = 10; (b1,b2,b3) = (2,5,8); Ui = log (xi/ bi+1) (C1,C2,C3) = (2,5,3) • Marginal utility weighted by contribution:CiUi’= Ci/(xi+ bi) • Pareto optimal • Solving the problem: • Maximize CiUi • Subject to •  xi · Ws • 0 · xi· bi8 i • Linear time complexity (x1,x2,x3) = (2,5,3)

17. (bi,Ci) (bj,Cj) (bk,Ck) .. ! (xi,xj,xk ..) U=log(x/b+1) Ws Resource Competition Games bi(t0) xi(t0) source node s competing node i time • Consider the competing node’s side: What is the optimal value of bi for node i ?

18. General game Resource competition game Players Competing nodes Strategies Bidding values Game rules Resource distribution mechanism Outcome Bandwidth allocated to nodes Resource Competition Games-- the theoretical game • Achieved game properties • Pareto optimality • Unique Nash equilibrium • Contribution proportional solution in equilibrium • Collusion proof

19. Resource Competition Games-- the Nash equilibrium • The Nash equilibrium (b* , x*) • bi* = xi* = (Ci /  Cj) Ws 8 i • Nash strategy for the previous example: b1*=2, b2*=5, b3*=3. • Verifications : • When bi* is decreased to be bi, by the desirability constraint, xi is at most bi. • When bi*is increased to be bi, xi does not increase.

20. 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.

21. Ws = 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 ] • Any new arrival or departure leads to a new equilibrium. • Proportional share in equilibrium. • No bandwidth wastage.

22. Ws = 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 • Equilibrium change due to the congestion. • Proportional sharing among un-congested nodes.

23. 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

24. Questions and Answers