game theory and pricing of internet services jean walrand wlr wlr (with linhai he & john...

Game Theory and Pricing of Internet

ServicesJean Walrand

http://www.eecs.berkeley.edu/~wlr

(with Linhai He & John Musacchio)

3Jean Walrand – MIT, January 27, 2005

Game Theory and Pricing of Internet Services

Motivation Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions References

TOC




TOC


Motivation Some users would pay for better

network services Fast occasional transfers (sync. databases,

backups, …) Videoconferences Streaming of presentations

These services are not available A large fraction of infrastructure is

poorly used: Wi-Fi access points Why?

TOC - Motivation


Motivation (continued)

Bandwidth? QoS Mechanisms? Protocols for requesting/provisioning

services? Economic Incentives for providing

services are lacking

TOC – Motivation


Motivation (continued)

Needed: Economic incentives Billing Mechanism Fair Revenue Sharing among

Providers Scalable Correct Incentives

Discourage cheating Promote upgrades

Revenues

Service Quality

increases improve

TOC Motivation




TOC


Three Problems

1. Service Differentiation Market segmentation Capture willingness to pay more for

better services

TOC – Three Problems


Three Problems (cont.)

2. Multiprovider Network

Incentives for better services through all providers Improved Services & Revenues

TOC – Three Problems


Three Problems (cont.)

3. Wi-Fi Access

Incentives to open private Wi-Fi access points Ubiquitous Access

TOC Three Problems




TOC


Service Differentiation

Model Examples Proposal

Joint work with Linhai He

TOC – Service Differentiation


Model

Two possible outcomes:

1. Users occupy different queues (delays = T1 & T2)

2. Users share the same queue (delay = T0)

If users do not randomize their choices, which one will

happen?

p1

p2

UsersA

B

H

L

TOC – Service Differentiation – Model

Each user chooses the service class i that maximizes his/her net benefit


Model (cont)p1

p2

A

B

H

L

H LB

H

L

A

f1(T0) – p2

f1(T1) – p1

f1(T2) – p2

f1(T0) – p1

A’s benefitT1 < T0 < T2

fi(.) nonincreasing

TOC – Service Differentiation Model

B’s benefitf2(T0) – p1 f2(T2) – p2

f2(T1) – p1 f2(T0) – p2


Example 1

H L

H

L

BA

9 – 4 = 59 – 4 = 5

9 – 1 = 89 – 1 = 8

14 – 4 = 105 – 1 = 4

5 – 1 = 414 – 4 = 10

p1

p2

A

B

H

L

f(T1) = 14f(T0) = 9f(T2) = 5

p1 = 4p2 = 1

TOC – Service Differentiation – Examples

Here, fi(.) = f(.)


Example 1

H L

H

L

BA

55

88

104

410

NE


Assume A picks H. Should B choose H or L?

Assume A picks H. Should B choose H or L?

Assume A picks H. B should choose H.Assume A picks H. B should choose H.

Assume A picks L. Should B choose H or L?

Assume A picks L. Should B choose H or L?

Assume A picks L. B should choose H.Assume A picks L. B should choose H. B H.B H.

Since B chooses H, A should also choose H.Since B chooses H, A should also choose H.

NE =

Nash

Eq

uili

bri

um


Example 1

H L

H

L

BA

NE


A and B choose H, get rewards equal to 5.If they had both chosen L, their rewards would have been 8!A and B choose H, get rewards equal to 5.If they had both chosen L, their rewards would have been 8!

Prisoner’s Dilemma!Prisoner’s Dilemma!

55

88

104

410


Example 2

H L

H

L

BA

9 – 49 - 4

9 – 19 - 1

13 – 45 - 1

7 – 111 - 4

p1

p2

A

B

H

L

T1: 13, 11T0: 9, 9T2: 7, 5

p1 = 4p2 = 1

No P

ure

Eq

uili

bri

um

f0 f1



Example 3 Extension to many users

Equilibrium exists if 9 0 s.t.

willingness to pay total load in class i

TOC – Service Differentiation Examples

(Indeed, )Also, the other users prefer L.

Note: T1 and T2 depend on the split of customers.

In this equilibrium, users with prefer H.


Example 3 Analysis of equilibriums:

inefficientequilibrium

unstableequilibrium

Here, f is a concave function and strict-priority scheduling is used.

TOC – Service Differentiation Examples

p1-p2

f(T1)-f(T2)


Proposal Dynamic Pricing

Fixed delay + dynamic price

•Provider chooses target delays for both classes

•Adjust prices based on demand to guarantee the delays

•Users still choose the class which maximizes their net benefit

TOC – Service Differentiation – Proposal


Proposal Recommendation: Dynamic Pricing

(cont)Why is it better?

•A Nash equilibrium exists•This equilibrium approximates the outcome of a Vickrey auction•If an arbitrator knows fi(T1) and fi(T2) from all users, Vickrey auction leads to socially efficient allocation•Approximation becomes exact when many users•Simpler to implement

TOC Service Differentiation – Proposal




TOC


Multiprovider Network Model Nash Game Revenue Sharing


TOC – Multiprovider Network


Model

+ p1

+ p2

p1+ p2

Monitor marks and processes inter-network billing

info

Pricing per packet

TOC – Multiprovider Network Model


Nash Game: Formulation

1 2p1 p2

D

• •

•

Demand=

d(p1+p2)C1 C2

• A game between two providers

• Different solution concepts may apply, depend

on actual implementation

• Nash game mostly suited for large networks

Provider 1 Provider 2

TOC – Multiprovider Network – Nash Game


Nash Game: Result

1. Bottleneck providers get more share of revenue than others

2. Bottleneck providers may not have incentive to upgrade

3. Efficiency decreases quickly as network size gets larger (revenues/provider drop with size)

TOC – Multiprovider Network Nash Game


Revenue Sharing Improving the game Model Optimal Prices Example

TOC – Multiprovider Network – Revenue Sharing


Revenue Sharing- Improving the Game

Possible Alternatives Centralized allocation Cooperative games Mechanism design

Our approach: design a protocol which overcomes drawbacks of non-cooperative

pricing is in providers’ best interest to follow is suitable for scalable implementation

TOC – Multiprovider Network – Revenue Sharing Improving


Revenue Sharing- Model Providers agree to share the revenue

equally, but still choose their prices independently

1 2p1 p2

D

• •

•

Demand=

d(p1+p2) C1 C2

Provider 1 Provider 2

TOC – Multiprovider Network – Revenue Sharing Model


Revenue Sharing- Optimal Prices

# of providers

Lagrange multiplier on link

i“locally optimal” total price for the

route

sum of prices charged by other

providers

A system of equations on prices

TOC – Multiprovider Network – Revenue Sharing – Optimal


Revenue Sharing- Optimal Prices (cont.)

For any feasible set of i, there is a unique solution:

On the link i with the largest , *), pi

* = N * + g(pi*)

On all other links, pj* = 0

Only the most congested link on a route sets its total price




{i} {pi*} {dr

*}

a Nash game with i as the strategy

It can be shown that a Nash equilibrium exists in this game.

Each provider solves its i based on local constraints




Comparison with social welfare maximization (TCP)

Social:

Sharing:

Incentive to upgrade Upgrade will always increase bottleneck

providers’ revenue

A tradeoff between efficiency and fairness




Efficient when capacities are adequate It is the same as that in centralized

allocation Revenue per provider strictly dominates

that in Nash game




A local algorithm for computing i

that can be shown to converge to Nash equilibrium:




1

i

d

hop count Nr=0

congestionprice r=0

flows on

route r

Nr=Nr+1r= max(r, i)

A possible scheme for distributed implementation

… ……

No state info needs to be kept by transit providers.

TOC – Multiprovider Network – Revenue Sharing Optimal


Example

C1=2 C2=5 C3=3

demand = 10 exp(-p2) on all routes

r1

r2

r3

r4

i

link 1

link 3

link 2

pricesp2

p3

p1

p4

TOC Multiprovider Network – Revenue Sharing – Example




TOC


Wi-Fi Pricing Motivation Web-Browsing File Transfer

TOC – Wi-Fi Pricing

Joint work with John Musacchio


Motivation Path to Universal WiFi Access

Massive Deployment of 802.11 base stations for private LANs

Payment scheme might incentivize base station owners to allow public access.

Direct Payments Avoid third party involvement. Transactions need to be “self enforcing”

Payments: Pay as you go: In time slot n,

- Base Station proposes price pn

- Client either accepts or walks away What are good strategies?

TOC – Wi-Fi Pricing Motivation


Web Browsing

Client Utility U = Utility per unit time

K = Intended duration of connection

Random variable in [0, 1]Known to client, not to BS

Random variable in {1, 2, …}Known to client, not to BS BS Utility

p1 + p2 + … + pN

U.min{K, N}

N = duration

TOC – Wi-Fi Pricing – Web Browsing


Web Browsing Theorem Perfect Bayesian Equilibrium:

Client accepts to pay p as long as p ≤ U

BS chooses pn = p* = arg maxp p P(U ≥ p)

Note: Surprising because BS learns about U …

TOC – Wi-Fi Pricing Web Browsing


File Transfer

Client Utility

K.1{K ≤ N}

BS Utility

p1 + p2 + … + pN

K = Intended duration of connectionRandom variable in {1, 2, …}Known to client, not to BS

N = duration

TOC – Wi-Fi Pricing – File Transfer


File Transfer TheoremPerfect Bayesian Equilibrium:

Client accepts to pay 0 at time n < K p ≤ K at time n = K

BS chooses a one-time-only payment

pay n* at time n* = arg maxn nP(K = n)

Note: True for bounded K. Proof by backward induction. Unfortunate ….

TOC – Wi-Fi Pricing – File Transfer




TOC


Conclusions

Dynamic Pricing to adjust QoS

Cooperative pricing -> distributed algorithm

Web browsing -> constant priceFile transfer -> one-time price

TOC – Conclusions


Conclusions

• Basic objective Improve revenues by better mechanisms for - service differentiation - pricing - revenue sharing

• Some preliminary ideas New pricing schemes - rational (equilibrium) - desirable incentives - implementable (scalable protocols)

TOC Conclusions




TOC


References

TOC References

Linhai He and Jean Walrand, "Pricing Differentiated Internet Services," INFOCOM 2005

Linhai He and Jean Walrand, "Pricing and Revenue Sharing Strategies for Internet Service Providers," INFOCOM 2005

John Musacchio and Jean Walrand, "Game-Theoretic Analysis of Wi-Fi Pricing," IEEE Trans. Networking, 2005


Thank you!

game theory and pricing of internet services jean walrand wlr wlr (with linhai he & john...

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