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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 Outline • Current Practices and Associated Problems • Our approach – A clean-slate multilateral settlement – Results – Implications • Future work and limitations What is an Internet Service Provider (ISP)? ISP objective: maximize profits • 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 routers customers Current ISP Business Practices Provider ISP Three levels of decisions • Interconnecting decision E • Routing decisions R (via BGP) • Bilateral financial settlements f Settlement f affects E, R Hot-potato Routing Customer/provider relationship Peering relationship Interconnection provider charges, customer withdrawal might want to save money Route change Source Destination Shortest Path Routing Customer ISP Customer ISP An ideal case of the ISPs’ decisions Route Topology Well-connected topology Fixed Revenue Backbone ISP 1 W=1 Local ISP 1 Local ISP 2 Peering links at Locally connect to bothboth backbone ISPs coasts Backbone ISP 2 A simple example: Two backbone ISPs Two local ISPs End-to-end service generates revenue The Cost Model x2/4 • 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. An ideal case of the ISPs’ decisions Route Topology Global Min Cost Well-connected topology Minimized routing cost and maximized profit Fixed CostRevenue | Profit Backbone ISP 1 x22/4 2/16 x Local 1ISP 1 x3 Local ISP 2 1/2 x42/8 x52/8 1/2 x62/16 x72/4 W=1 2/16 x82/16 A simple example: Two backbone ISPs Two local ISPs End-to-end service generates revenue We normalize the total required Backbone ISP 2traffic intensity to be 1. Problems with the current practice Topology Well-connected Balkanization topology Increased profit profit Minimized routing routing and costreduced and maximized Route Topology Global Min Cost Cost | Profit x22/4 x12/16 x32/16 1/2 x42/8 x52/8 1/2 x62/16 x72/4 x82/16 An example: 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! e.g. Backbone ISPs charge local ISPs. Problems with the current practice Topology Balkanization Increased routing and reduced profit Further profit reduction from routing inefficiency Route Topology Global Hot Min Cost Potato Cost | Profit x22/4 x12/16 1/2 x42/8 x52/8 1/2 1 x72/4 x82/16 An example: 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! Problem 2: ISPs route selfishly to maximize profits! e.g. upper backbone ISP wants to use hot-potato routing to reduce its routing cost. Problems summary: selfish interconnecting and routing Global Ideal case: cooperative ISPs Route Topology Cost | Profit (maximized) Global Min Cost Connectivity wellconnected ISPs selfishly interconnect Route Topology Cost | Profit (reduced) Global Min Cost Connectivity Balkanized ISPs selfishly route traffic Route Hot Potato Topology Cost | Profit (further reduced) Connectivity Balkanized Our solution: A clean-slate multilateral settlement Provider ISP Recall: three levels of decisions • Interconnecting decision E • Routing decisions R •Multilateral Bilateral financial settlements j f j collects revenue from customers jSettlement redistributes profitsE,toRISPs f affects E, R follow from j $$ $$$ Customer/provider relationship j(E,R) $$ Peering relationship Customer ISP Our solution: A clean-slate multilateral settlement Each ISP’s local interconnecting and routing decisions. Given: j Local decisions: Ei,Ri Objective: to maximize Ei Ri ji(E,R) The Shapley value mechanism j Revenue Worth function v(S) on any subset of ISPs. Routing cost v( ) = 0.8125 v( ) = 0.625 v( x22S: /4 D (S). Marginal contribution ISP i to set of ISPs i D ( x12/16 x32/16 ) = v( ) - v( 1/2 ) = 0.1875 x42/8 D ( ) = v( x62/16 ) - v( x52/8 1= 0.625 )1/2 x72/4 x82/16 Profit: v(S) )=0 The Shapley value mechanism j 1 ∑ D (S(p,i)) i ji = N! p ∈ p S(p, N: total # of ISPs, e.g. N=3 : set of N! orderings S(p,i): set of ISPs in front of ISP i ) D (S(p, )) j( )=2.4/6=0.4 Empty v( )=0 v( )=0 Empty v( )- v( )=0.2 v( )- v( )=0.6 v( )-v( )=0.8 v( )-v( )=0.8 Results: incentive for optimal routing Route Topology Hot Global Local Potato Min Cost Recall the inefficiency situation Cost | Profit j x22/4 x12/16 Profit maximized increase 1/4 1/2 x42/8 E.g. the upper ISP wants to minimize local routing cost x52/8 3/4 1/2 1 x7 2/4 Shapley mechanism distributions profit x82/16 Best strategy for all ISPs: global min cost routing ISPs route selfishly to maximize profits! Results: incentive for using optimal routes • Given any fix interconnecting topology, 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 result: Selfish local behavior coincides with global optimal solution! Results: incentive for interconnecting Route Topology Global Min Cost Recall: the best strategy for all ISPs is to use global min cost routes. Cost | Profit x22/4 x1 Profit increase 2/16 x3 2/16 E.g. the left local ISP connects to the low backbone ISP. 5/12 1/2 x42/8 x52/8 1/2 7/12 x62/16 x72/4 j x82/16 Further the right local ISP connects to the upper backbone ISP. Profit increase ISPs interconnect selfishly to maximize profits! 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, 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: Summary Route Topology Under bilateral settlements, ISPs interconnect and route selfishly Cost | Profit Connectivity Hot Potato Balkanized j solves the selfish interconnecting problem Route Topology ISPs have incentive to use optimal routes Cost | Profit j Global Min Cost Balkanized j solves the selfish routing problem Route Global Min Cost Connectivity Topology ISPs have incentive to interconnect Cost | Profit j Connectivity wellconnected Future Work and Limitations • Computational Complexity • Information Structure – Limited information – Centralized mechanism versus distributed mechanism • Trust Issues