Richard Ma, Sam Lee, John Lui (CUHK) David Yau (Purdue) 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 Ci Bidding value bi Allocated bandwidth xi Actual receiving bandwidth xi’ node i

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)

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 = Ws otherwise xi = bi 8 i.

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.

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

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

Resource Distribution Mechanisms: Incentive-based Contribution weighted filling Pareto optimal Solving the problem: Maximize  Cixi Subject to  xi · Ws 0 · xi · bi 8 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)

Resource Distribution Mechanisms : Utility concerns Utility concern for nodes. Denote Ui(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.

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 · bi 8 i Linear time complexity (x1,x2,x3) = (2,5,3)

Resource Competition Games bi(t0) (bi,Ci) (bj,Cj) (bk,Ck) .. Ws U=log(x/b+1) ! (xi,xj,xk ..) 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 ?

Resource Competition Games -- the theoretical game General game Resource competition game Players Competing nodes Strategies Bidding values Game rules Resource distribution mechanism Outcome Bandwidth 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*) 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.

Practical game issues Common knowledge problem Wastage 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.

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.

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.

Conclusions Service differentiations Equilibrium solution 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

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