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 Presented by Xie Chengwu

Outline Cooperative Framework Profit Distribution Mechanism Incentive For Optimal Routing Incentive For Interconnecting Implementation and Conclusion

Cooperative Framework Three Layers of the Current Internet and a Novel Two-Stage Settlement Model Network Model

Three Layers of the Current Internet Bottom layer, pairs of ISPs decide whether or not to connect. They decide the venue and type of the connections. middle layer, each ISP advertises BGP routes to neighboring ISPs and decides how to route traffic efficiently to reduce its own cost. At the top layer, end-users pay their local ISPs for the services

Three Layers of the Current Internet Fig. A view of ISP interactions of the Internet.

a Novel Two-Stage Settlement Model S1) Customers make service agreements at their local ISPs S2a) All payments from customers are collected by a multilateral profit distribution mechanism, which decides the proportion of revenue each ISP receives. S2b) Knowing the rule of the profit distribution mechanism,each ISP makes local decisions on interconnection and routing to maximize its profit.

a Novel Two-Stage Settlement Model Fig. A two-stage multilateral settlement model.

Network Model Router-Level Model:(N,v,M,E,R) Remark: N: the set of ASs v: worth function M: the set of routers in the network. E: the set of directed links connecting the routers R: a flow profile used by the ASs to route traffic G(M,E) defines the router-level topology of the network. G(N,E’) defines the AS-level topology

Fig. A router-level model and its corresponding AS-level topology.

Worth Function We define the worth function to be the profit v(S)=V 0 (S) – V C (S) V 0 (S) is the revenue function V C (S) is the cost function, given any flow profile, we define the cost function as the following: S is any nonempty subset of N

Profit Distribution Mechanism Definition : A profit distribution mechanism is an operator φ on a network system (N ， v) that assigns a profit vector φ (N,v)= ( φ 1, …, φ N ). Each φ i (N,v) denotes the assigned profit of AS i.

Profit Distribution Mechanism Desirable Properties Efficiency profit received from the services; no extra Symmetry 2 ASs contribute the same => receive the same profit Fairness AS i contribution to j equals j to i Dummy no contribution => no profit Strong monotonicity contributes more, receives more Additivity sum of the profits from individual services

Shapley Value Mechanism Shapley Value: S(π,i ） is the set of players preceding i in the orderingπ.

Incentive For Optimal Routing the set of optimal flow profiles defined as the following: The set of optimal routing strategies of AS is defined by

Incentive For Optimal Routing Theorem 1 (Optimal Routing):Given any flow profile, by applying an optimal routing strategy, AS i maximizes its profit under the Shapley value mechanism. Corollary 1: Under the Shapley value mechanism, every optimal routing strategy is a Nash equilibrium.

Incentive For Optimal Routing Theorem 2 (Profit Decomposition): For each AS, the Shapley value profit can be decomposed into a Myerson value on the AS-level topology and a Shapley value on the routing cost:

Examples Customers of router 1 on thewest coast need to communicate with customers of router 4 on the east coast. the revenue and required traffic intensity to be1. The costs on intra-AS paths and inter-AS paths shown in the fig.

Examples (b)hot-potato routing strategy (c) chooses the feasible flow (d) optimal flow profiles is the AS k’s shapley profit

Fig Hot-potato routing versus optimal routing

Incentive For Interconnecting Definition: An extended flow profile maps each coalition to a feasible flow on the induced directed subgraph or a zero vector. the set of optimal extended flow profiles optimal extended routing strategies for AS i

Incentive For Interconnecting Corollary: Under the Shapley-value mechanism, every optimal extended routing strategy is a Nash equilibrium. Theorem : Any AS i that has profit is a dummy AS, and there exists an optimal extended flow profile that does not route through AS for all.

Incentive For Interconnecting Definition : An AS is called a veto AS, if for all in Every veto AS is essential in order to generate the profit for any coalition. Theorem: For any veto AS i of the system, we have for any

Incentive For Interconnecting Theorem (Incentive for Interconnection): In the system, suppose and are two routers belonging to ASs i and j. If and are not directly connected (e.g., ), then adding the interconnection between and achieves no lesser profits for both AS

Examples veto AS is good, dummy is bad dummy

Implementation Issues Traffic and Topology Information ASs might not want to reveal their internal structures, and router-to- router traffic intensity measurements might not be feasible Truth Revealing this mechanism requires knowledge of the true revenue and cost of each ISP

Example of Optimal Routing in Practice Fig.. Routes from Columbia to Global Crossing during May 2007

Example of Optimal Routing in Practice Fig.. Revenue distribution for the ISPs.

Conclusion profit is "fairly" shared EfficiencyFairnessOptimal RoutingInterconnections Incentives

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