The Shapley Value: Its Use and Implications on Internet Economics

Richard T.B. Ma

Columbia University

Dah-ming Chiu, John C.S. Lui

The Chinese University of Hong Kong

Vishal Misra, Dan Rubenstein

Columbia University

Outline

• ISP Practices and Associated Problems

• Profit Sharing and Shapley Value

• Shapley Mechanism and Incentive Properties

• Future work

What is an Internet Service Provider (ISP)?

• The Internet is composed of Autonomous Systems (ASes).

• An ISP is a business entity.– Might comprise multiple ASes.– Provide Internet access.

– Objective: maximize profits.

ISP

• Eyeball ISPs– Provide Internet access to customers:– Place Large investment in infrastructure.– E.g. AT&T, Verizon …

• Content ISPs– Provide contents via the Internet.– Serve customers like:

• Transit ISPs– Tier 1 ISPs: global connectivity of the Internet.– Provide transit services for other ISPs.– Cover a large geographic area.

Different classes of players

Service Differentiation Information Neutrality

Net Neutrality Debate: Whether or not to provider Service Differentiation?

Network Balkanization: De-peering between ISPs

Level 3 Cogent

ISP Settlement Problems: a Macro Perspective

How to appropriately share profits among ISP?

Transit Eyeball

Transit Transitzero-dollar peering

Content Providers

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

Shortest Path Routing

Hot-potato Routing

Source

Destination

Peering relationship

Customer/provider relationship

Provider ISP

Customer ISPCustomer ISP

Settlement affects E, R

provider charges, customer might want

to save money

Interconnection withdrawal

Route change

ISP Practices: a Micro Perspective

• Consider a PC market with only one operating system provider and one micro-processor provider.

• Egalitarian profit sharing:

Profit V= Revenue - Cost

How to share profit? -- the baseline case

j( )=j( ) = V21

• Symmetry: two micro-processor providers obtain the same profit.

• Efficiency: summation of three companies’ profit equal V.

• Balanced Contribution:

How to share profit? -- more players

j( )=j( )

j( )+j( )+j( ) = V

j( ) - V = j( ) - 021

32

V 61

V

61

V

• The unique solution (Shapley value) that satisfies Efficiency Symmetry and Balanced Contribution:

B1

B2

Bn

C2

C1

Cm

j(B )= V, j(C ) = Vm(n+m)

nn(n+m)

m

How to share profit? -- eyeball and content ISPs

• Intuitions and explanations– The more of the same kind provide substitutions.

– The less of a kind can obtain more leverage.

C2

C1

Cm

B1

B2

Bn

j(B )= V, j(C ) = Vm(n+m)

nn(n+m)

m

Results and implications of ISP profit sharing

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

number of ISPs of its type.

– Proportional to the number of ISPs of the opposite type.

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

Peering relationship

Customer/provider relationship

Provider ISP

Customer ISP

Settlement affects E, R

The Shapley value settlementsj

j(E,R)$$$

$$

$$

jcollects revenue from customers

jredistributes profits to ISPs

E, R follow from j

A clean-slate multilateral settlement

Local decisions: Ei,Ri

Ei

Ri

Given:j

Objective: to maximizeji(E,R)

Each ISP makes local interconnecting and routing decisions.

Individual ISP’s selfish behavior

• Assumptions:– Aggregate Profit = Total Revenue – Total Routing Cost.– Profits are distributed via the Shapley value solution.– Fixed interconnecting topology.– ISPs locally decide routes to maximize their profits.

• Theorem (Incentive for routing): Any ISP maximizes its profit 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.

Surprise: Selfish local behavior coincides with global optimal solution!

Incentive results -- optimal routing

Incentive results -- interconnecting

• Assumptions:– Aggregate Profit = Total Revenue – Total Routing Cost.– Profits are distributed via the Shapley value solution.– For any topology, ISPs use global min-cost routes.– ISPs locally decide interconnections to maximize their profits.

• Theorem (Incentive for interconnecting): Both interconnecting ISPs 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.

Summary

• Ideal profit-sharing solution – the Shapley value– Efficiency, Symmetry and Balanced Contribution.

– Additivity, Strong Monotonicity, Dummy …

– Close-form solution for eyeball/content ISPs.

• ISP incentives under the Shapley value solution– Incentive to use global optimal routes.

– Incentive to interconnect.

Future Work and New Results

X$

X₤

B2

B3

B1

B2

US

UK

{♫, ♣}

{♣}

{♫}

C2

C1

C3

• Include Transit ISPs

• General Internet Topology

• Implications for Bilateral Agreements among ISPs

T1T2

T3T4