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Internet Economics: the use of Shapley value for ISP settlement 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 Current Practices and Associated Problems Our approach –A clean-slate multilateral settlement –Results –Implications Future work and limitations

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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. –Autonomous sub-network –Provide Internet access –Maximize profits ISP customers routers ISP objective: maximize profits

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Current ISP Business Practices 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 ISP Settlement affects E, R provider charges, customer might want to save money Interconnection withdrawal Route change

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

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The Cost Model x 2 /4 Assumptions –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.

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x 2 2 /4 x 7 2 /4 x 4 2 /8 x 5 2 /8 x 1 2 /16 x 6 2 /16 x 3 2 /16 x 8 2 /16 1/2 RouteTopology Global Min Cost An ideal case of the ISPs’ decisions Two backbone ISPs Two local ISPs End-to-end service generates revenue 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 intensity to be 1. Minimized routing cost and maximized profit

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x 2 2 /4 x 7 2 /4 x 4 2 /8 x 5 2 /8 x 1 2 /16 x 6 2 /16 x 3 2 /16 x 8 2 /16 1/2 RouteTopology Global Min Cost Problems with the current practice Cost | Profit Problem 1: ISPs interconnect selfishly to maximize profits! e.g. Backbone ISPs charge local ISPs. An example: Well-connected topology Minimized routing cost and maximized profit Topology Balkanization Increased routing and reduced profit Two backbone ISPs Two local ISPs End-to-end service generates revenue Routing costs on links, e.g. bandwidth and maintenance

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x 2 2 /4 x 7 2 /4 x 4 2 /8 x 5 2 /8 x 1 2 /16 x 8 2 /16 1/2 RouteTopology Global Min Cost Cost | Profit Hot Potato 1 Problems with the current practice An example: Topology Balkanization Increased routing and reduced profit Problem 2: ISPs route selfishly to maximize profits! e.g. upper backbone ISP wants to use hot-potato routing to reduce its routing cost. Further profit reduction from routing inefficiency Two backbone ISPs Two local ISPs End-to-end service generates revenue Routing costs on links, e.g. bandwidth and maintenance Problem 1: ISPs interconnect selfishly to maximize profits!

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Problems summary: selfish interconnecting and routing Global Ideal case: cooperative ISPs RouteTopologyCost | Profit (maximized)Connectivity Global Min Cost well- connected RouteTopologyCost | Profit (reduced)Connectivity Global Min Cost Balkanized RouteTopologyCost | Profit (further reduced)Connectivity Hot Potato Balkanized ISPs selfishly route traffic ISPs selfishly interconnect

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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 Our solution: A clean-slate multilateral settlement Multilateral financial settlements (E,R)(E,R) $$$ $$ collects revenue from customers redistributes profits to ISPs E, R follow from

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Local decisions: E i,R i EiEi RiRi Given: Objective: to maximize i (E,R) Our solution: A clean-slate multilateral settlement Each ISP’s local interconnecting and routing decisions.

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Marginal contribution ISP i to set of ISPs S: i (S). The Shapley value mechanism Worth function v(S) on any subset of ISPs. Revenue Routing cost Profit: v(S) x 2 2 /4 x 7 2 /4 x 4 2 /8 x 5 2 /8 x 1 2 /16 x 8 2 /16 1 v( ) = 0v( ) = x 6 2 /16 v( ) = x 3 2 /16 1/2 ( ) = v( ) -v( ) = v( ) -v( ) = ( ) =

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

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x 2 2 /4 x 7 2 /4 x 4 2 /8 x 5 2 /8 x 1 2 /16 x 8 2 /16 RouteTopology Results: incentive for optimal routing Cost | Profit Local Min Cost 1 Hot Potato 1/4 3/4 1/2 Global Min Cost Recall the inefficiency situation Shapley mechanism distributions 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

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Given any fix interconnecting topology, ISPs can locally decide routing strategies {R i * } to maximize their profits. Theorem (Incentive for routing): Any ISP i can maximize its profit i 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: incentive for using optimal routes Surprising result: Selfish local behavior coincides with global optimal solution!

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x 2 2 /4 x 7 2 /4 x 4 2 /8 x 5 2 /8 x 1 2 /16 x 8 2 /16 RouteTopology Results: incentive for interconnecting Cost | Profit 1/2 Global Min Cost x 6 2 /16 7/12 5/12 x 3 2 /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 Further the right local ISP connects to the upper backbone ISP.

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For any topology, a global optimal route R * is used by all ISPs. ISPs can locally decide interconnecting strategies {E i * } to maximize their profits. Theorem (Incentive for interconnecting): By interconnecting, both 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. Results: incentive for interconnecting

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Results: Summary Under bilateral settlements, ISPs interconnect and route selfishly RouteTopologyCost | ProfitConnectivity Global Min Cost well- connected RouteTopologyCost | ProfitConnectivity Global Min Cost Balkanized RouteTopologyCost | ProfitConnectivity Hot Potato Balkanized ISPs have incentive to interconnect ISPs have incentive to use optimal routes solves the selfish interconnecting problem solves the selfish routing problem

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Future Work and Limitations Computational Complexity Information Structure –Limited information –Centralized mechanism versus distributed mechanism Trust Issues

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