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

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

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

Service Differentiation

Model Examples Proposal

Joint work with Linhai He

TOC – Service Differentiation

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?

UsersA

TOC – Service Differentiation – Model

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

Model (cont)p1

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

9 – 4 = 59 – 4 = 5

9 – 1 = 89 – 1 = 8

14 – 4 = 105 – 1 = 4

5 – 1 = 414 – 4 = 10

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

p1 = 4p2 = 1

TOC – Service Differentiation – Examples

Here, fi(.) = f(.)

Example 1

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. 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.

Example 1

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!

Example 2

9 – 49 - 4

9 – 19 - 1

13 – 45 - 1

7 – 111 - 4

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

p1 = 4p2 = 1

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

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

Multiprovider Network Model Nash Game Revenue Sharing

TOC – Multiprovider Network

p1+ p2

Monitor marks and processes inter-network billing

Pricing per packet

TOC – Multiprovider Network Model

Nash Game: Formulation

1 2p1 p2

• •

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

• •

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

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:

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

link 1

link 3

link 2

pricesp2

TOC Multiprovider Network – Revenue Sharing – Example

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

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

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...

toc toc motivation slide

toc toc motivation slide

better services toc

jean walrand mit

john musacchio slide

service class i

wifi access incentives

game theory

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