A Game Theoretic Approach to Provide Incentive and Service Differentiation in

P2P Networks

John C.S. LuiThe Chinese University of Hong Kong

Joint work with Richard T.B. Ma, Sam C.M. Lee, David K.Y. Yau (Purdue University)

Outline

• Problem, Issues & System Infrastructure

• Resource Distribution Mechanisms• Resource Competition Games• Experiments• Future work

Problems• The popularity of P2P applications• Free-riding problem

– Nearly 70% users do not share.

• Tragedy of the Commons– Nearly 50% request responses are from top 1% nodes.

• Nodes enjoy service without contribution.

• Objectives– Provide incentive for user to share.– Provide Service Differentiation for

(physically and habitually) different users.

Technical issues• How to provide incentives to users?

– Contribution measure.– Differentiated service.

• How to distribute bandwidth resource?– Various physical types & contributions.– Fairness, efficiency concern.

• How to adapt network dynamics?– Join / leave.– Network congestion.

System Infrastructure: terms

•Contribution value Ci

•Bidding value (or desired bandwidth) bi

•Allocated bandwidth xi

•Actual receiving bandwidth xi

’

node i

System Infrastructure: Interactions

time

bi(t0)

xi (t0)

xi

(t1)

(bi,Ci

)(bj,Cj) (bk,Ck) ..

bi(t1)competing node i

source node s

xi’

(t1)

xi’

(t0)

Ws

Outline

• Problem and System Infrastructure

• Resource Distribution Mechanisms

• Resource Competition Games• Experiments

Resource Distribution Mechanisms (RDM)

• Objective– Design an appropriate resource distribution

function: f : {Ci}×{bi} → {xi} .

– Design an efficient algorithm to achieve the resource distribution.

• Desired Properties and Constraints– Physical constraint on individual bandwidth: xi ¸ 0 .

– Physical constraint on the total bandwidth resource: xi · Ws .

– The assigned bandwidth resource should less than or equal to the request desired bandwidth (desirability constraint): xi · bi .

– Pareto optimality: bi ¸ Ws ! xi = Ws .

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.

x1

x2

x3

(0,0,0)

(10,0,0)

(10,0,0)

(10,0,0)

Ws = x1 + x2 + x3 = 10

(0,5,8)

0 · xi · bi

(2,0,8)(0,0,8)

(2,5,8)

(2,0,0)

(0,5,0) (2,5,0)

• Non-negative constraint

• Budget constraint• Desirability

constraint

• Pareto optimal

Ws = 10; (b1,b2,b3) = (2,5,8)

Resource Distribution Mechanisms: Baseline

algorithm• Progressive filling

algorithm• Pareto optimal• Solving the

problem:– Maximize xi

– Subject to • xi · Ws

• 0 · xi · bi 8 i

• Max-min fairness

2

5

8

Ws = 10; (b1,b2,b3) = (2,5,8)

(x1,x2,x3) = (2,4,4)

(2,2,2)

(2,4,4)

x1

x2

x3

(0,0,0)

(10,0,0)

(10,0,0)

(10,0,0)

Ws = x1 + x2 + x3 = 10

(0,5,8)

0 · xi · bi

(2,0,8)(0,0,8)

(2,5,8)

(2,0,0)

(0,5,0) (2,5,0)

Resource Distribution Mechanisms

• Desired Properties (Cont.)– Incentive: large Ci values induce

large xi .

• Idea: progressive filling weighted by Ci .

– Social utility: Ui .

•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-

based• Contribution

weighted filling • Pareto optimal• Solving the problem:

– Maximize Cixi

– Subject to • xi · Ws

• 0 · xi · bi 8 i

• Proportional to contribution values

(C1,C2,C3) = (2,5,3)

(x1,x2,x3) = (2,5,3)

Ws = 10; (b1,b2,b3) = (2,5,8)

1

8/3

1

52 3

(2,5,3)

x1

x2

x3

(0,0,0)

(10,0,0)

(10,0,0)

(10,0,0)

Ws = x1 + x2 + x3 = 10

(0,5,8)

0 · xi · bi

(2,0,8)(0,0,8)

(2,5,8)

(2,0,0)

(0,5,0) (2,5,0)

Resource Distribution Mechanisms: Utility-based

• Maximal Marginal Utility first filling: U’i = 1/(xi+bi)

• Pareto optimal• Solving the problem:

– Maximize Ui

– Subject to • xi · Ws

• 0 · xi · bi 8 i

• Same marginal utility.

Ui = log (xi/bi+1)

Ws = 10; (b1,b2,b3) = (2,5,8)

(x1,x2,x3) = (2,5,3)

2

5

8

2

5

8

x1

x2

x3

(0,0,0)

(10,0,0)

(10,0,0)

(10,0,0)

Ws = x1 + x2 + x3 = 10

(0,5,8)

0 · xi · bi

(2,0,8)(0,0,8)

(2,5,8)

(2,0,0)

(0,5,0) (2,5,0)

(2,3,0)(2,3,5)

Resource Distribution Mechanisms: Incentive and

Utility• Contribution

weighted marginal utility filling CiUi

’.

• Pareto optimal• Solving the

problem:– Maximize CiUi

– Subject to • xi · Ws

• 0 · xi · bi 8 I

Ws = 10; (b1,b2,b3) = (2,5,8);

Ui = log (xi/bi+1)

(C1,C2,C3) = (2,5,3)

(x1,x2,x3) = (2,5,3)

2 5 3

1 1

8/31 1

8/3

x1

x2

x3

(0,0,0)

(10,0,0)

(10,0,0)

(10,0,0)

Ws = x1 + x2 + x3 = 10

(0,5,8)

0 · xi · bi

(2,0,8)(0,0,8)

(2,5,8)

(2,0,0)

(0,5,0) (2,5,0)

(2,5,3)

2

5

8

1

8/3

1

52 3

2

5

8

2

5

8

2 5 3

1 1

8/31 1

8/3

• Incentive and utility concern– If Ci/bi >= Cj/bj

Ui>=Uj

• Efficiency – Pareto optimal

• Easy to implementation– Linear time complexity

Outline

• Problem and System Infrastructure

• Resource Distribution Mechanisms

• Resource Competition Games

• Experiments

Resource Competition Games

• Consider the competing node’s side.

– What is the optimal value of bi for node i to send?

time

bi(t0)

xi (t0)competing node i

source node s

(bi,Ci)

(bj,Cj) (bk,Ck) ..

Ws

U=log(x/b+1)! (xi,xj,xk ..)

Resource Competition Games

-- the theoretical game

• General Game– Players– Strategies– Game rules– Outcome

• Resource Competition Game– Competing nodes– Biddings– Resource distribution

mechanism– Amount of bandwidth

resource

Resource Competition Games-- the theoretical game

• Solution Concepts– Pareto optimality : No other solution which

makes some of the players better off without hurting any of the other players.

– Nash equilibrium : No player can get better off by unilaterally shifting strategy from Nash equilibrium.

• Resource competition game results– The resource distribution mechanism

guarantees Pareto optimality.– There exists a unique Nash equilibrium

solution.– In the unique Nash equilibrium, solution is

proportional to contribution values.– Collusion proof.

Resource Competition Games-- the theoretical game

• The Nash equilibriumbi

* = WsCi / Cj 8 i ! xi* =

WsCi / Cj 8 i (in the paper)

• Justifications for Nash equilibrium– When bi < bi

*, by budget constraint, xi is at most bi .

– When bi > bi*, xi does not

increase.

2 5

1 1

1 1

3

1

1

3

3/4

3/4

3

1.5

1

Ws = 10; (b1,b2,b3) = (2,5,8); Ui = log (xi/bi+1) (C1,C2,C3) = (2,5,3)

Resource Competition Games

-- the practical game• Gaps between the theoretical game and the practical game.

• 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.

Resource Competition Games

-- the practical game• When a new node i requests service:

– The source node tells the current signal information si = WsCi / Cj to the new participant i.

– Competing node bids for bi = min{ wi,(1+)si }

• Service period:– Competing node measures the effective

bandwidth xi’ it receives.

– Competing node bids for bi = min{ wi,(1+)xi’ }

Practical game: Justifications

• Source node’s signal si = WsCi / Cj helps operating around the Nash equilibrium.

• bi = min{wi,(1+)si} or bi = min{wi,(1+)xi’}

– Even the new xi > wi, the competing node cannot receive due to the physical constraint.

– Large bidding value may decrease the resource gain.

– Adaptive to network congestion.• value

– Facilitate competing nodes reaching new equilibrium due to network dynamics.

– Larger value of , faster convergence to new equilibrium.

– Smaller value of , less oscillation in new equilibrium.

Resource Competition Games

-- the practical game• Dynamic equilibrium

– If the bottleneck is on competing nodes’ side:8 i 2 N xi

* = wi

– If the bottleneck is on any intermediate link:8 j 2 N xj

* = vj

– If the bottleneck is on the source node’s side: 8 k 2 N xk

* = (Ck / { l 2 N} Cl ) Ws’ where Ws

’

=Ws - { i 2 N} wi - { j 2 N} vj)

Outline

• Problem and System Infrastructure

• Resource Distribution Mechanisms

• Resource Competition Games

• Experiments

• Future work

• Proportional bandwidth gain corresponding to the contribution.

• New equilibrium reaches immediately.

• Bandwidth allocation is bounded by the maximal receiving bandwidth.

Ws = 2 (Mbps) Contribution: [ 400, 100, 200, 300 ]

Maximal receiving bandwidth: [ 2, 1.5, 1, 0.5 ] (Mbps)

Arrival time: [ 20, 40, 60, 80 ]

• Changes of equilibrium by arrival and departure.

• Proportional share and physical limits.

• No bandwidth wastage.

• Departure leads to new equilibrium by .

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 ]

• Changes of equilibrium during the congestion.

• Proportional sharing among un-congested nodes.

Ws = 2 (Mbps) Contribution: [ 400, 300, 200, 100 ]

Maximal receiving bandwidth: [ 2, 1.5, 1, 0.5 ] (Mbps)

Congestion period: [ 30, 40 ] & [ 50, 60 ] and has a maximal receiving bandwidth of 0.4 Mbps during the congestion

period.

Experiments: conclusion

• 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