1. 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)

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 = Ws otherwise xi = bi 8 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
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)

12. 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)

14. 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.

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

17. 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 ?

18. 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

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 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.

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 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

24. Questions and Answers