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A Shapley Value Perspective on Internet Economics

A Shapley Value Perspective on Internet Economics. 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

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A Shapley Value Perspective on Internet Economics

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  1. A Shapley Value Perspective on Internet Economics Vishal Misra Department of Computer Science Columbia University Joint work with Richard TB Ma, Dah-Ming Chiu, John Lui and Dan Rubenstein

  2. 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

  3. Building blocks of the Internet: ISPs • 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.

  4. Three types of ISPs • Eyeball ISPs: • Provide Internet access to individual users. • E.g. TimeWarner • Content ISPs: • Provide contents on the Internet. • Transit ISPs: • Tier 1 ISPs: global connectivity of the Internet. • Provide transit services for other ISPs.

  5. A motivating example • Win-win: • Content provider finds customers • Customers get content • ISPs obtain revenue Fixed charge Volume-based charge

  6. What happens with P2P traffic? • Win-lose under P2P paradigm: • Content provider pays less • Customers get faster download • Content ISP obtains less revenue • Eyeball ISPs handle more traffic • Consequence: • ISPs want to avoid P2P traffic

  7. Engineering solutions and … beyond • Proposed engineering solutions: • Strategy of ISPs: Limit P2P traffic rate • Counter-strategy of users: Encryption • Counter-strategy of ISPs: Deep packet inspection • A new/global angle: Network Economics • Goal: a win-win/fair solution • Issue: how do we design algorithms/protocols to achieve it? • Consequence: • ISPs want to avoid P2P traffic

  8. Other important problems that can be looked at 1. Network Neutrality Debate: Content-based Service Differentiation ? Yes No Legal/regulatory policy for the Internet industry. Some ISPs dominate or ISPs cannot survive. Suppress the development of the Internet. 2. Network Balkanization: Break-ups of Connected ISPs 15% of Internet unreachable Level 3 Cogent Not only a technical/operation problem, but also economic issues. Threatens the global connectivity of the Internet.

  9. Other important problems that can be looked at • A new/global angle: Network Economics • Goal: a win-win/fair solution • Issues: how do we design algorithms/protocols to achieve it?

  10. 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.

  11. How to share profit? -- the baseline case • One content and one eyeball ISP • Profit V = total revenue = content-side + eyeball-side • Win-win/fair profit sharing:

  12. Unique solution (Shapley value) 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 Win-win/fair properties:

  13. Myerson 1977 Efficiency Symmetry Fairness Shapley Value Shapley 1953 Efficiency Symmetry Dummy Additivity Young 1985 Efficiency Symmetry StrongMonotonicity History and properties of the Shapley value What is the Shapley value? – A measure of one’s contribution to different coalitions that it participates in.

  14. How to share profit? -- n symmetric eyeball ISPs • Theorem: the Shapley profit sharing solution is

  15. Results and implications of profit sharing • 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.

  16. Profit share -- multiple eyeball and content ISPs • Theorem: the Shapley profit sharing solution is

  17. Results and implications of ISP profit sharing • 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. • Intuition • The larger group of ISPs provides redundancy. • The smaller group of ISPs has leverage.

  18. Profit share -- eyeball, transit and content ISPs • Intuition • The larger group of ISPs provides redundancy. • The smaller group of ISPs has leverage. • Theorem: the Shapley profit sharing solution is

  19. Profit share – general topologies 1. Shapley values under sub-topologies: Theorem: Dynamic Programming！ 2. Whether the profit can still be generated:

  20. ISP business practices: a macro perspective Two forms of bilateral settlements: 2. Zero-Dollar Peering Provider ISPs $$$ $$$ 1. Customer-Provider Settlement Customer ISPs

  21. $ $ $ $ $ $ Implications – the value chain $ $ $ Eyeball-side Revenue $ Content-side Revenue $ $ $ $ $ $ $ $

  22. $ $ $ $ $ $ Implications – the value chain Eyeball-side Revenue $ Content-side Revenue $ $ $ $ $ • Shapley value suggested revenue flows: • Content-side revenue: Content Transit Eyeball • Eyeball-side revenue: Eyeball Transit Content

  23. $ $ $ $ $ $ Implications – equivalent bilateral settlements Eyeball-side Revenue $ Content-side Revenue Providers $ $ Customers Customers Zero-dollar Peering $ $ $ • When CR ≈ BR, bilateral implementations: • Customer-Provider settlements (Transit ISPs as providers) • Zero-dollar Peering settlements (between Transit ISPs) • Stable structure when local ISPs are homogeneous.

  24. $ $ $ $ $ $ Implications – equivalent bilateral settlements $ $ $ $ $ $ $ $ $ Eyeball-side Revenue $ $ $ $ $ $ Customer Provider Paid Peering Content-side Revenue $ $ $ • If CR >> BR, bilateral implementations: • Reverse Customer-Provider (Transits compensate Eyeballs) • Paid Peering (Content-side compensates eyeball-side) • New settlements will emerge to maintain a stable structure.

  25. 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. • Answer: The Shapley value. • How do wefind 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.

  26. Recap: ISP practices from a macro perspective Two current forms of bilateral settlements: Two new forms of bilateral settlements: 2. Zero-Dollar Peering 3. Inverse Customer-Provider Settlement 4. Paid Peering 1. Customer-Provider Settlement

  27. 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. • Answer: The Shapley value. • How to find it? Complex ISPs structure, computationally expensive. • Result: Closed-form solution 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 do we induce good behavior? Selfish behavior may hurt other ISPs. • What is the impact on the entire network? Equilibrium is efficient?

  28. Current ISP Business Practices: A Micro Perspective Provider ISP • Three levels of ISP decisions • Interconnecting decision E • Routing decisions R (via BGP) • Bilateral settlements f Interconnection withdrawal Settlement faffects E, R Customer-Provider Settlements provider charges high Route change Hot-potato Routing Source Destination Zero-Dollar Peering Shortest Path Routing Customer ISP Customer ISP

  29. W = 1 An ideal case of the ISP decisions Well-connected topology Fixed Revenue Backbone ISP 1 Local ISP 1 Local ISP 2 A simple example: Peering links at both coasts Locally connect to both backbone ISPs Two backbone ISPs Two local ISPs End-to-end service generates revenue Routing costs on links Backbone ISP 2

  30. 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.

  31. W = 1 An ideal case of the ISP decisions Global Min Cost Well-connected topology MIN routing cost and MAX profit Fixed Revenue Cost|Profit Backbone ISP 1 x22/4 x12/16 x32/16 Local ISP 1 Local ISP 2 1/2 A simple example: Two backbone ISPs Two local ISPs End-to-end service generates revenue Routing costs on links x42/8 x52/8 1/2 x62/16 x82/16 x72/4 We normalize the total required traffic load to be 1. Backbone ISP 2

  32. Problems with the current practice Global Min Cost Topology Balkanization Well-connected topology Increased routing and reduced profit MIN routing cost and MAX profit Cost|Profit x22/4 x12/16 x32/16 1/2 A simple example: Two backbone ISPs Two local ISPs End-to-end service generates revenue Routing costs on links x42/8 x52/8 1/2 x62/16 x82/16 x72/4 Behavior 1: ISPs interconnect selfishly to maximize profits! e.g. Backbone ISPs charge local ISPs.

  33. Problems with the current practice Global Min Cost Hot Potato Topology Balkanization Increased routing and reduced profit Cost|Profit Profit reduction by routing inefficiency x22/4 x12/16 1/2 A simple example: Two backbone ISPs Two local ISPs End-to-end service generates revenue Routing costs on links x42/8 x52/8 1/2 1 x82/16 x72/4 Behavior 1: ISPs interconnect selfishly to maximize profits! Behavior 2: ISPs route selfishly to maximize profits! e.g. upper backbone ISP wants to use hot-potato routing to reduce its routing cost.

  34. Issues of Current ISP Settlement: A Micro Perspective Global Ideal case: cooperative ISPs ISPs selfishly interconnect ISPs selfishly route traffic How to encourage ISPs to operate at efficient/optimal points?

  35. $$$ j(E,R) $$ $$ Our solution: The Shapley Mechanism j Provider ISP • Recall: three levels of ISP decisions • Interconnecting decision E • Routing decisions R • Bilateral settlements f Multilateral settlements j jcollects revenue from customers jdistributes profits to ISPs Settlement faffects E, R Customer-Provider Settlements Source Destination Zero-Dollar Peering Customer ISP Customer ISP

  36. Our solution: The Shapley Mechanism j Each ISP’s local interconnecting and routing decisions. Given:j Local decisions:Ei,Ri Objective: to maximizeji(E,R) Ei Ri

  37. Results: Routing Incentive Hot Potato Global Min Cost Local Min Cost j Recall the inefficiency situation Cost|Profit x22/4 Shapley mechanism distributes profit x12/16 Profit maximized Profit increase 1/4 1/2 E.g. the upper ISP wants to minimize local routing cost x42/8 x52/8 1 3/4 1/2 Best strategy for all ISPs: global min cost routing x82/16 x72/4 ISPs route selfishly to maximize profits!

  38. Results: Incentives for using Optimal Routes • 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. Surprising! Local selfish behaviors coincide with global optimal solution!

  39. Results: Interconnecting Incentive Global Min Cost j Recall: the best strategy for all ISPs is to use global min cost routes. Cost|Profit x22/4 Profit increase x12/16 x32/16 E.g. the left local ISP connects to the low backbone ISP. 5/12 1/2 x42/8 x52/8 1/2 7/12 Further the right local ISP connects to the upper backbone ISP. x62/16 x82/16 x72/4 Profit increase ISPs interconnect selfishly to maximize profits!

  40. Results: Incentive for Interconnecting • 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.

  41. Micro perspective ISP settlement: result summary Selfishly interconnect and route j solves the selfish interconnecting problem ISPs have incentive to use optimal routes j j solves the selfish routing problem ISPs have incentive to interconnect j

  42. 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. • 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

  43. Myerson 1977 Efficiency Symmetry Fairness Shapley 1953 Efficiency Symmetry Dummy Additivity Young 1985 Efficiency Symmetry StrongMonotonicity New Application and Properties of the Shapley Value Shapley Value: Contributions to Coalitions Ma et al. 2008 Ma et al. 2007 ISP Routing Incentive ISP Profit Sharing ISP Interconnecting Incentive • Guideline for • ISPs: negotiate stable and incentive settlements. • Governments: make regulatory policy for the industry.

  44. 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

  45. v( ) =0.8125 D ( ) = v( ) = 0.625 D ( ) = v( ) - v( ) = 0.1875 v( ) = 0 v( ) = 0.625 v( ) - The Shapley value mechanism j Revenue Profit v(S) is defined on any subset of ISPs Profit = Revenue - Cost Routing cost Profit: v(S) x22/4 Marginal contribution of ISP i to set of ISPs S: Di(S). x12/16 x32/16 1/2 x42/8 x52/8 1 1/2 x62/16 x82/16 x72/4

  46. S(p, ) j( )=2.4/6=0.4 p D(S(p, )) v( )=0 v( )=0 Empty Empty v( )- v( )- v( )=0.2 v( )=0.6 v( )=0.8 v( )=0.8 v( )- v( )- The Shapley value mechanism j N: total # of ISPs, e.g. N=3 P: set of N! orderings S(p,i): set of ISPs in front of ISP i

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