A Shapley Value Perspective on Internet Economics Paris Networking Workshop 2009 Vishal Misra Department of Computer Science Columbia University Joint

A Shapley Value Perspective on Internet Economics

Paris Networking Workshop 2009

Vishal Misra

Department of Computer Science

Columbia University

Joint work with

Richard TB Ma, Dah-Ming Chiu, John Lui and Dan Rubenstein

Outline

• Network economics research and problems

• Our research: two problems– Design Efficient and Fair Profit Sharing Mechanisms– Encourage ISPs to operate at efficient/optimal points

ISP ISPISP

• The Internet is operated by hundreds of interconnected Internet Service Providers (ISPs).

• An ISP is a autonomous business entity– Provide Internet services.– Common objective: to make profit.

Building blocks of the Internet: ISPs

ISP ISPISP

Three types of ISPs

• Eyeball ISPs:– Provide Internet access to individual users.– E.g. TimeWarner, Free

• Content ISPs:– Provide contents on the Internet.

• Transit ISPs:– Tier 1 ISPs: global connectivity of the

Internet.– Provide transit services for other ISPs.

BC T

A motivating example

ISPB

$5/Gb

ISPB

$50/month

$50/month

ISPB

$50/month

ISPC

• Win-win under Client-Server:– Content providers find customers– Users get information– ISPs obtain revenue

Volume-based charge

Fixed-rate charge

ISPC

What happens with P2P traffic?

$5/Gb

ISPB

$50/month

$50/month

ISPB

$50/month

• Win-lose under P2P paradigm:– Content providers pay less– Customers get faster downloads– Content ISP obtains less revenue– Eyeball ISPs handle more traffic

• In reality: P2P is a nightmare for ISPs.

ISPB

Engineering solutions and … beyond

• Proposed engineering approaches:– ISPs: Drop P2P packets based on port number– Users: Dynamic port selection– ISPs: Deep packet inspection– Users: Disguise by encryption– ISPs: Behavioral analysis

• A new/global angle: Network Economics– Goal: a win-win/fair solution for all.– Related Issues:

• What is a win-win/fair solution? How do we find it?• How do we design algorithms/protocols to achieve?

Two important issues of the Internet

ISPB

ISPC

ISPT

ISPT

1. Network Neutrality Debate: Content-based Service Differentiation ?

Yes No

2. Network Balkanization: Break-up of connected ISPs

15% of Internet unreachableLevel 3 Cogent

Legal/regulatory policy for the Internet industry: Allow or Not?

Not a technical/operation problem, but an economic issue of ISPs.

Allow: ISPs might dominate; Not allow: ISPs might die.

Either way, suppress the development of the Internet.

Threatens the global connectivity of the Internet.

Other important problems that can be looked at

ISPB

ISPC

ISPT

ISPT

• A new/global angle: Network Economics– Goal: a win-win/fair solution– Issues: how do we design algorithms/protocols to achieve it?

Problems we try to solve

• Problem 1: Find a win-win/fair profit-sharing solution for ISPs.• Challenges

– What’s the solution? ISPs don’t know, even with best intentions.

– How do we find it? Complex ISPs structure, computationally expensive.

– How do we implement it? Need to be implementable for ISPs.

• One content and one eyeball ISP

• Profit V = total revenue = content-side + eyeball-side

• Win-win/fair profit sharing:

C1 B1

How to share profit? -- the baseline case

j = j = V21

B1 C1

How to share profit? – two symmetric eyeball ISPs

• Symmetry: same profit for symmetric eyeball ISPs

• Efficiency: summation of individual ISP profits equals v

• Fairness: same mutual contribution for any pair of ISPs

j = j = jB1 B2 B

j + 2j = VC1 B

Unique solution (Shapley value)

j = VC1 3

2

61j = VB

Win-win/fair properties:

B1j - V = j - 0

C1 21

C1

B2

B1

History and properties of the Shapley value

Shapley Value

Efficiency Symmetry Fairness

Myerson 1977

Efficiency Symmetry Dummy Additivity

Shapley 1953

Efficiency Symmetry Strong Monotonicity

Young 1985

What is the Shapley value? – A measure of one’s contribution to different coalitions that it participates in.

How do we share profit? -- n symmetric eyeball ISPs

• Theorem: the Shapley profit sharing solution is

j = V, j = Vn+1n

n(n+1)1

B C

C1

B2

B1

Bn

Results and implications of profit sharing

C1

B1

Bn-1

• More eyeball ISPs, the content ISP gets larger profit share.– Users may choose different eyeball ISPs;

however, must go through content ISP,– Multiple eyeball ISPs provide redundancy ， – The single content ISP has leverage.

• Content’s profit with one less eyeball: • The marginal profit loss of the content ISP:

If an eyeball ISP leaves– The content ISP will lose 1/n2 of its profit.– If n=1, the content ISP will lose all its profit.

j = V, j = Vn+1n

n(n+1)1

B C

Bn

nn-1j’ = VC

Dj = V - V = - j n+1n

nn-1 1

n2C C

Profit share -- multiple eyeball and content ISPs

C2

C1

Cm

B1

B2

Bn


j = V, j = Vn(n+m)m

m(n+m)n

CB

Results and implications of ISP profit sharing

• Intuition– The larger group of ISPs provides redundancy.– The smaller group of ISPs has leverage.

C2

C1

Cm

B1

B2

Bn

• Each ISP’s profit share is– Inversely proportional to the

number of ISPs of its own type. – Proportional to the number of

ISPs of the opposite type.

j = , j = nm

(n+m)V n

m(n+m)V

B C

Sm=1

m

Sk=1

k

n+m+kV ( )m

m ( )kk ( )n+m+k-1

m+kj =

Sn=1

n

Sk=1

k

n+m+kV ( )n

n ( )kk ( )n+m+k-1

n+kj =

Sm=1

m

Sn=1

n

n+m+kV ( )m

m ( )nn ( )n+m+k-1

m+nj =

B

C

T

C2

C1

Cm

B1

B2

Bn

T2

T1

Tk

Profit share -- eyeball, transit and content ISPs

• Intuition– The larger group of ISPs provides redundancy.– The smaller group of ISPs has leverage.


Profit share – general topologies

B2

B1

C1 T1

jC1 = [0 + V + V + V] = V41

31

31

125

ji = [S ji(N \{j}) + V{i is veto}]j≠iN

1

jC1 = 0

B2

B1

C1 T1

jC1 = 1/3V

B2

B1

C1 T1

jC1 = 1/3V

B2

B1

C1 T1

1. Shapley values under sub-topologies:

C1 is veto.

B2

B1

C1 T1

2. Whether the profit can still be generated:

Theorem:

Dynamic Programming ！

Current ISP Business Practices: A Macroscopic View

Zero-Dollar Peering

Customer-Provider Settlement

Two forms of bilateral settlements:

ISPT

ISPT

ISPB

ISPC

Provider ISPs

Customer ISPs

$$$$$$

T1

T2

T3

T4

C2

C1

C3

B2

B3

B1

B2

Eyeball ISPsContent

ISPsTransit ISPs

Achieving the win-win/fair profit share

$ $$

$ $

$ $

$$

$ $$

$

$

$$ $$

Content-side Revenue

Eyeball-side Revenue

T1

T2

T3

T4

C2

C1

C3

B2

B3

B1

B2

Eyeball ISPsContent

ISPsTransit ISPs

Achieving the win-win/fair profit share

• Two revenue flows to achieve the Shapley profit share:– Content-side revenue: Content Transit Eyeball– Eyeball-side revenue: Eyeball Transit Content

$ $$

$ $$

$ $$

$$$



T1

T2

T3

T4

C2

C1

C3

B2

B3

B1

B2

Eyeball ISPsContent

ISPsTransit ISPs

Achieving Shapley solution by bilateral settlements

$ $$

$ $$

$ $$

$$$

• When CR ≈ BR, bilateral implementations:– Customer-Provider settlements (Transit ISPs as

providers)– Zero-dollar Peering settlements (between Transit ISPs)– Current settlements can achieve fair profit-share for ISPs.

Providers

CustomersCustomers

Zero-dollarPeering



T1

T2

T3

T4

C2

C1

C3

B2

B3

B1

B2

Eyeball ISPsContent

ISPsTransit ISPs

Achieving Shapley solution by bilateral settlements

$ $$

$ $ $

$ $$

$$$

$ $$

$ $ $$ $$

$ $ $

• If CR >> BR, bilateral implementations:– Reverse Customer-Provider (Transits compensate Eyeballs)– Paid Peering (Content-side compensates eyeball-side)– New settlements are needed to achieve fair profit-share.

Customer Provider

Paid Peering



ISPT

Recap: ISP Practices from a Macroscopic View

Zero-Dollar Peering

Customer-Provider Settlement

Two current forms of bilateral settlements:

ISPT

ISPC

Reverse Customer-Provider Settlement

Paid Peering

Our Implication: Two new forms of bilateral settlements:

ISPB

Next, a Microscopic View to inspect on ISP behaviors

$$$

$$$



– What’s the solution? ISPs don’t know, even with best intentions.– Answer: The Shapley value.– How do we find it? Complex ISPs structure, computationally

expensive.– Result: Closed-form solution and Dynamic Programming. – How do we implement it? Need to be implementable for ISPs.– Implication: New bilateral settlements.



– What’s the solution? ISPs don’t know, even with best intentions.– Answer: The Shapley value.– How do we find it? Complex ISPs structure, computationally

expensive.– Result: Closed-form solution and Dynamic Programming. – How do we implement? Need to be implementable for ISPs.– Implication: New bilateral settlements.

• Problem 2: Encourage ISPs to operate at efficient/optimal points.• Challenges

– How do we induce good behavior? Selfish behavior may hurt other ISPs.

– What is the impact on the entire network? Equilibrium is efficient?

Current ISP Business Practices: A Micro Perspective

Three levels of ISP decisions• Interconnecting decision E• Routing decisions R (via BGP)• Bilateral settlements f

Shortest Path Routing

Hot-potato Routing

Source

Destination Zero-DollarPeering

Customer-Provider Settlements

Provider ISP

Customer ISP Customer ISP

Settlement f affects E, R

provider charges high

Interconnection withdrawal

Route change

Peering links atboth coasts

Locally connect to

both backbone ISPs

Route TopologyAn ideal case of the ISP decisions

Two backbone ISPsTwo local ISPsEnd-to-end service

generates revenueRouting costs on links

Backbone ISP 1

Backbone ISP 2

Local ISP 1 Local ISP 2

Fixed Revenue

A simple example:

Well-connected topology

W = 1

Routing cost model

x2/4

• Assumptions (based on current practices)– Routing costs on links, e.g. bandwidth capacity and

maintenance.– Going across the country is more expensive.– More expensive when link is more congested.

• Costs increase with link loads– Standard queueing theory results.– Capital investment for upgrades.

x22/4

x72/4

x42/8 x5

2/8

x12/16

x62/16

x32/16

x82/16

1/2

1/2

Route Topology

Global Min Cost

An ideal case of the ISP decisions



Backbone ISP 1

Backbone ISP 2

Local ISP 1 Local ISP 2

Fixed RevenueCost | Profit

A simple example:

Well-connected topology

W = 1

We normalize the total required traffic load to be 1.

MIN routing cost and MAX profit

x22/4

x72/4

x42/8 x5

2/8

x12/16

x62/16

x32/16

x82/16

1/2

1/2

Route Topology

Global Min Cost

Problems with the current practice

Cost | Profit

Behavior 1: ISPs interconnect selfishly to maximize profits!e.g. Backbone ISPs charge local ISPs.



A simple example:

MIN routing cost and MAX profitIncreased routing and reduced profitWell-connected topologyTopology Balkanization

x22/4

x72/4

x42/8 x5

2/8

x12/16

x82/16

1/2

1/2

Route Topology

Global Min Cost

Cost | Profit

Hot Potato

1

Problems with the current practice

Behavior 2: ISPs route selfishly to maximize profits!e.g. upper backbone ISP wants to use hot-potato routing to reduce its routing cost.

Profit reduction by routing inefficiency

Behavior 1: ISPs interconnect selfishly to maximize profits!

Topology BalkanizationIncreased routing and reduced profit



A simple example:

Issues of Current ISP Settlement: A Micro Perspective

Global Ideal case: cooperative ISPs

Route Topology Cost | Profit (maximized) Connectivity

Global Min Cost

Well-connected

Route Topology Cost | Profit (reduced) Connectivity

Global Min Cost

Balkanized

Route Topology Cost | Profit (further reduced) Connectivity

Hot Potato

Balkanized

ISPs selfishly route traffic

ISPs selfishly interconnect

How to encourage ISPs to operate at efficient/optimal points?

j collects revenue from customers

j distributes profits to ISPs

Our solution: The Shapley Mechanism j

Recall: three levels of ISP decisions• Interconnecting decision E• Routing decisions R• Bilateral settlements f

Source

Destination Zero-DollarPeering

Customer-Provider Settlements

Provider ISP

Customer ISP Customer ISP

Settlement f affects E, R

Multilateral settlements j

j(E,R)$$$

$$

$$

Local decisions: Ei,Ri

Ei

Ri

Given: j

Objective: to maximize ji(E,R)

Our solution: The Shapley Mechanism jEach ISP’s local interconnecting and routing decisions.

x22/4

x72/4

x42/8 x5

2/8

x12/16

x82/16

Route TopologyResults: Routing Incentive

Cost | Profit

Local Min Cost

1

Hot Potato

j

1/4

3/4

1/2

1/2

Global Min Cost

Recall the inefficiency situation

Shapley mechanism distributes profit

ISPs route selfishly to maximize profits!

E.g. the upper ISP wants to minimize local routing cost

Best strategy for all ISPs: global min cost routing

Profit increaseProfit maximized

• Given any fixed interconnecting topology E, ISPs can locally decide routing strategies {Ri

*} to maximize their profits.

• Theorem (Incentive for routing): Any ISP i can maximize its profit ji by locally minimizing the global routing cost.

– Implication: ISPs adapt to global min cost routes.

• Corollary (Nash Equilibrium): Any global min cost routing decision is a Nash equilibrium for the set of all ISPs.

– Implication: global min cost routes are stable.

Results: Incentives for using Optimal Routes

Surprising! Local selfish behaviors coincide with global optimal solution!

x22/4

x72/4

x42/8 x5

2/8

x12/16

x82/16

Route TopologyResults: Interconnecting Incentive

Cost | Profit j

1/2

1/2

Global Min Cost

x62/16

7/12

5/12

x32/16

ISPs interconnect selfishly to maximize profits!

Recall: the best strategy for all ISPs is to use global min cost routes.

E.g. the left local ISP connects to the low

backbone ISP.

Profit increase

Profit increase

Further the right local ISP connects to the upper backbone ISP.

• For any topology, a global optimal route R* is used by all ISPs. ISPs can locally decide interconnecting strategies {Ei

*} to maximize their profits.

• Theorem (Incentive for interconnecting): By interconnecting, ISPs will have non-decreasing profits.

– Implication: ISPs have incentive to interconnect.– Does not mean: All pairs of ISPs should be connected.

• Redundant links might not reduce routing costs.• Sunk cost is not considered.

Results: Incentive for Interconnecting

Micro perspective ISP settlement: result summarySelfishly interconnect and route

Route Topology Cost | Profit Connectivity

Global Min Cost

well-connected


Global Min Cost

Balkanized


Hot Potato

Balkanized

ISPs have incentive to interconnect

ISPs have incentive to use optimal routes

j

j

j solves the selfish interconnecting problem

j solves the selfish routing problem



– What’s the solution? ISPs don’t know, even with best intentions.– Answer: The Shapley value– How to find it? Complex ISPs structure, computationally expensive.– Result: Closed-form sol. and Dynamic Programming– How to implement? Need to be implementable for ISPs.– Implication: New bilateral settlements

• Problem 2: Encourage ISPs to operate at efficient/optimal points.• Challenges

– How to induce good behavior? Selfish behavior may hurt other ISPs.– Answer: The Shapley mechanism – Result: Incentives for optimal routes and interconnection – What is the impact of the entire network? Equilibrium is efficient?– Result: Optimal global Nash equilibrium

• Guideline for – ISPs: negotiate stable and incentive settlements.– Governments: make regulatory policy for the industry.

New Application and Properties of the Shapley Value

Shapley Value: Contributions to Coalitions

Efficiency Symmetry Fairness

Myerson 1977

Efficiency Symmetry Dummy Additivity

Shapley 1953

Efficiency Symmetry Strong Monotonicity

Young 1985

ISP Routing Incentive

ISP Interconnecting Incentive

Ma et al. 2007

ISP Profit Sharing

Ma et al. 2008

Related Publications

• Richard T.B. Ma, Dahming Chiu, John C.S. Lui, Vishal Misra and Dan Rubenstein, On Cooperative Settlement Between Content, Transit and Eyeball Internet Service Providers, Proceedings of 2008 ACM Conference on Emerging network experiment and technology (CoNEXT 2008), Madrid, Spain, December, 2008

• Richard T.B. Ma, Dahming Chiu, John C.S. Lui, Vishal Misra and Dan Rubenstein, The Shapley Value: Its Use and Implications on Internet Economics, Allerton Conference on Communication, Control and Computing, September, 2008

• Richard T.B. Ma, Dah-ming Chiu, John C.S. Lui, Vishal Misra and Dan Rubenstein, Interconnecting Eyeballs to Content: A Shapley Value Perspective on ISP Peering and Settlement, ACM NetEcon, Seattle, WA, August, 2008

• Richard T.B. Ma, Dahming Chiu, John C.S. Lui, Vishal Misra and Dan Rubenstein, Internet Economics: The use of Shapley value for ISP settlement, Proceedings of 2007 ACM Conference on Emerging network experiment and technology (CoNEXT 2007), Columbia University, New York, December, 2007

p

j( )=2.4/6=0.4Empty

S( , p )

Empty

1N! ∈

∑ Di (S(,i))ji =

D (S(p, ))

v( )=0

v( )=0.2v( )-

v( )-v( )=0.8

v( )=0

v( )-v( )=0.8

v( )=0.6v( )-

N: total # of ISPs, e.g. N=3P: set of N! orderings

S(p,i): set of ISPs in front of ISP i

The Shapley value mechanism j

Documents

A Shapley Value Perspective on Internet Economics Paris Networking Workshop 2009 Vishal Misra Department of Computer Science Columbia University Joint