The Shapley Value: Its Use and Implications on Internet Economics

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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

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Outline

• ISP Practices and Associated Problems
• Profit Sharing and Shapley Value
• Shapley Mechanism and Incentive Properties
• Future work

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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
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Different classes of players

• Eyeball ISPs
• Provide Internet access to customers
• Place Large investment in infrastructure.
• E.g. ATT, 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.

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ISP Settlement Problems a Macro Perspective
Net Neutrality Debate Whether or not to provider
Service Differentiation?
Service Differentiation
Information Neutrality
Eyeball
Content Providers
Transit
Network Balkanization De-peering between ISPs
Transit
Transit
zero-dollar peering
How to appropriately share profits among ISP?
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ISP Practices a Micro Perspective
Provider ISP

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

Settlement f affects E, R
provider charges, customer might want to save
money
Interconnection withdrawal
Hot-potato Routing
Customer/provider relationship
Route change
Peering relationship
Source
Destination
Shortest Path Routing
Customer ISP
Customer ISP
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How to share profit? -- the baseline case

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

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How to share profit? -- more players

• Symmetry two micro-processor providers obtain
  the same profit.
• Efficiency summation of three companies profit
  equal V.
• Balanced Contribution

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How to share profit? -- eyeball and content ISPs

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

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Results and implications of ISP profit sharing

• Each ISPs profit is
• Inversely proportional to the number of ISPs of
  its type.
• Proportional to the number of ISPs of the
  opposite type.

• Intuitions and explanations
• The more of the same kind provide substitutions.
• The less of a kind can obtain more leverage.

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A clean-slate multilateral settlement
Provider ISP

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

The Shapley value settlements j
j collects revenue from customers j
redistributes profits to ISPs E, R follow from j
Settlement f affects E, R
Customer/provider relationship
Peering relationship
Customer ISP
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Individual ISPs selfish behavior
Each ISP makes local interconnecting and routing
decisions.
Given j
Local decisions Ei,Ri
Objective to maximize ji(E,R)
Ei
Ri
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Incentive results -- optimal routing

• 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!
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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.

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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.

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Future Work and New Results

• Include Transit ISPs
• General Internet Topology
• Implications for Bilateral Agreements among ISPs