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