a shapley value perspective on internet economics paris networking workshop 2009 vishal misra...
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A Shapley Value Perspective on Internet Economics
Paris Networking Workshop 2009
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– Design Efficient and Fair Profit Sharing Mechanisms– Encourage ISPs to operate at efficient/optimal points
ISP ISPISP
• 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.
Building blocks of the Internet: ISPs
ISP ISPISP
Three types of ISPs
• Eyeball ISPs:– Provide Internet access to individual users.– E.g. TimeWarner, Free
• Content ISPs:– Provide contents on the Internet.
• Transit ISPs:– Tier 1 ISPs: global connectivity of the
Internet.– Provide transit services for other ISPs.
BC T
A motivating example
ISPB
$5/Gb
ISPB
$50/month
$50/month
ISPB
$50/month
ISPC
• Win-win under Client-Server:– Content providers find customers– Users get information– ISPs obtain revenue
Volume-based charge
Fixed-rate charge
ISPC
What happens with P2P traffic?
$5/Gb
ISPB
$50/month
$50/month
ISPB
$50/month
• Win-lose under P2P paradigm:– Content providers pay less– Customers get faster downloads– Content ISP obtains less revenue– Eyeball ISPs handle more traffic
• In reality: P2P is a nightmare for ISPs.
ISPB
Engineering solutions and … beyond
• Proposed engineering approaches:– ISPs: Drop P2P packets based on port number– Users: Dynamic port selection– ISPs: Deep packet inspection– Users: Disguise by encryption– ISPs: Behavioral analysis
• A new/global angle: Network Economics– Goal: a win-win/fair solution for all.– Related Issues:
• What is a win-win/fair solution? How do we find it?• How do we design algorithms/protocols to achieve?
Two important issues of the Internet
ISPB
ISPC
ISPT
ISPT
1. Network Neutrality Debate: Content-based Service Differentiation ?
Yes No
2. Network Balkanization: Break-up of connected ISPs
15% of Internet unreachableLevel 3 Cogent
Legal/regulatory policy for the Internet industry: Allow or Not?
Not a technical/operation problem, but an economic issue of ISPs.
Allow: ISPs might dominate; Not allow: ISPs might die.
Either way, suppress the development of the Internet.
Threatens the global connectivity of the Internet.
Other important problems that can be looked at
ISPB
ISPC
ISPT
ISPT
• A new/global angle: Network Economics– Goal: a win-win/fair solution– Issues: how do we design algorithms/protocols to achieve it?
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.
• One content and one eyeball ISP
• Profit V = total revenue = content-side + eyeball-side
• Win-win/fair profit sharing:
C1 B1
How to share profit? -- the baseline case
j = j = V21
B1 C1
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
j = j = jB1 B2 B
j + 2j = VC1 B
Unique solution (Shapley value)
j = VC1 3
2
61j = VB
Win-win/fair properties:
B1j - V = j - 0
C1 21
C1
B2
B1
History and properties of the Shapley value
Shapley Value
Efficiency Symmetry Fairness
Myerson 1977
Efficiency Symmetry Dummy Additivity
Shapley 1953
Efficiency Symmetry Strong Monotonicity
Young 1985
What is the Shapley value? – A measure of one’s contribution to different coalitions that it participates in.
How do we share profit? -- n symmetric eyeball ISPs
• Theorem: the Shapley profit sharing solution is
j = V, j = Vn+1n
n(n+1)1
B C
C1
B2
B1
Bn
Results and implications of profit sharing
C1
B1
Bn-1
• 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.
j = V, j = Vn+1n
n(n+1)1
B C
Bn
nn-1j’ = VC
Dj = V - V = - j n+1n
nn-1 1
n2C C
Profit share -- multiple eyeball and content ISPs
C2
C1
Cm
B1
B2
Bn
• Theorem: the Shapley profit sharing solution is
j = V, j = Vn(n+m)m
m(n+m)n
CB
Results and implications of ISP profit sharing
• Intuition– The larger group of ISPs provides redundancy.– The smaller group of ISPs has leverage.
C2
C1
Cm
B1
B2
Bn
• 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.
j = , j = nm
(n+m)V n
m(n+m)V
B C
Sm=1
m
Sk=1
k
n+m+kV ( )m
m ( )kk ( )n+m+k-1
m+kj =
Sn=1
n
Sk=1
k
n+m+kV ( )n
n ( )kk ( )n+m+k-1
n+kj =
Sm=1
m
Sn=1
n
n+m+kV ( )m
m ( )nn ( )n+m+k-1
m+nj =
B
C
T
C2
C1
Cm
B1
B2
Bn
T2
T1
Tk
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
Profit share – general topologies
B2
B1
C1 T1
jC1 = [0 + V + V + V] = V41
31
31
125
ji = [S ji(N \{j}) + V{i is veto}]j≠iN
1
jC1 = 0
B2
B1
C1 T1
jC1 = 1/3V
B2
B1
C1 T1
jC1 = 1/3V
B2
B1
C1 T1
1. Shapley values under sub-topologies:
C1 is veto.
B2
B1
C1 T1
2. Whether the profit can still be generated:
Theorem:
Dynamic Programming !
Current ISP Business Practices: A Macroscopic View
Zero-Dollar Peering
Customer-Provider Settlement
Two forms of bilateral settlements:
ISPT
ISPT
ISPB
ISPC
Provider ISPs
Customer ISPs
$$$$$$
T1
T2
T3
T4
C2
C1
C3
B2
B3
B1
B2
Eyeball ISPsContent
ISPsTransit ISPs
Achieving the win-win/fair profit share
$ $$
$ $
$ $
$$
$ $$
$
$
$$ $$
Content-side Revenue
Eyeball-side Revenue
T1
T2
T3
T4
C2
C1
C3
B2
B3
B1
B2
Eyeball ISPsContent
ISPsTransit ISPs
Achieving the win-win/fair profit share
• Two revenue flows to achieve the Shapley profit share:– Content-side revenue: Content Transit Eyeball– Eyeball-side revenue: Eyeball Transit Content
$ $$
$ $$
$ $$
$$$
Content-side Revenue
Eyeball-side Revenue
T1
T2
T3
T4
C2
C1
C3
B2
B3
B1
B2
Eyeball ISPsContent
ISPsTransit ISPs
Achieving Shapley solution by bilateral settlements
$ $$
$ $$
$ $$
$$$
• When CR ≈ BR, bilateral implementations:– Customer-Provider settlements (Transit ISPs as
providers)– Zero-dollar Peering settlements (between Transit ISPs)– Current settlements can achieve fair profit-share for ISPs.
Providers
CustomersCustomers
Zero-dollarPeering
Content-side Revenue
Eyeball-side Revenue
T1
T2
T3
T4
C2
C1
C3
B2
B3
B1
B2
Eyeball ISPsContent
ISPsTransit ISPs
Achieving Shapley solution by bilateral settlements
$ $$
$ $ $
$ $$
$$$
$ $$
$ $ $$ $$
$ $ $
• If CR >> BR, bilateral implementations:– Reverse Customer-Provider (Transits compensate Eyeballs)– Paid Peering (Content-side compensates eyeball-side)– New settlements are needed to achieve fair profit-share.
Customer Provider
Paid Peering
Eyeball-side Revenue
Content-side Revenue
ISPT
Recap: ISP Practices from a Macroscopic View
Zero-Dollar Peering
Customer-Provider Settlement
Two current forms of bilateral settlements:
ISPT
ISPC
Reverse Customer-Provider Settlement
Paid Peering
Our Implication: Two new forms of bilateral settlements:
ISPB
Next, a Microscopic View to inspect on ISP behaviors
$$$
$$$
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 we find 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.
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 we find it? Complex ISPs structure, computationally
expensive.– Result: Closed-form solution and Dynamic Programming. – How do we 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?
Current ISP Business Practices: A Micro Perspective
Three levels of ISP decisions• Interconnecting decision E• Routing decisions R (via BGP)• Bilateral settlements f
Shortest Path Routing
Hot-potato Routing
Source
Destination Zero-DollarPeering
Customer-Provider Settlements
Provider ISP
Customer ISP Customer ISP
Settlement f affects E, R
provider charges high
Interconnection withdrawal
Route change
Peering links atboth coasts
Locally connect to
both backbone ISPs
Route TopologyAn ideal case of the ISP decisions
Two backbone ISPsTwo local ISPsEnd-to-end service
generates revenueRouting costs on links
Backbone ISP 1
Backbone ISP 2
Local ISP 1 Local ISP 2
Fixed Revenue
A simple example:
Well-connected topology
W = 1
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.
x22/4
x72/4
x42/8 x5
2/8
x12/16
x62/16
x32/16
x82/16
1/2
1/2
Route Topology
Global Min Cost
An ideal case of the ISP decisions
Two backbone ISPsTwo local ISPsEnd-to-end service
generates revenueRouting costs on links
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 load to be 1.
MIN routing cost and MAX profit
x22/4
x72/4
x42/8 x5
2/8
x12/16
x62/16
x32/16
x82/16
1/2
1/2
Route Topology
Global Min Cost
Problems with the current practice
Cost | Profit
Behavior 1: ISPs interconnect selfishly to maximize profits!e.g. Backbone ISPs charge local ISPs.
Two backbone ISPsTwo local ISPsEnd-to-end service
generates revenueRouting costs on links
A simple example:
MIN routing cost and MAX profitIncreased routing and reduced profitWell-connected topologyTopology Balkanization
x22/4
x72/4
x42/8 x5
2/8
x12/16
x82/16
1/2
1/2
Route Topology
Global Min Cost
Cost | Profit
Hot Potato
1
Problems with the current practice
Behavior 2: ISPs route selfishly to maximize profits!e.g. upper backbone ISP wants to use hot-potato routing to reduce its routing cost.
Profit reduction by routing inefficiency
Behavior 1: ISPs interconnect selfishly to maximize profits!
Topology BalkanizationIncreased routing and reduced profit
Two backbone ISPsTwo local ISPsEnd-to-end service
generates revenueRouting costs on links
A simple example:
Issues of Current ISP Settlement: A Micro Perspective
Global Ideal case: cooperative ISPs
Route Topology Cost | Profit (maximized) Connectivity
Global Min Cost
Well-connected
Route Topology Cost | Profit (reduced) Connectivity
Global Min Cost
Balkanized
Route Topology Cost | Profit (further reduced) Connectivity
Hot Potato
Balkanized
ISPs selfishly route traffic
ISPs selfishly interconnect
How to encourage ISPs to operate at efficient/optimal points?
j collects revenue from customers
j distributes profits to ISPs
Our solution: The Shapley Mechanism j
Recall: three levels of ISP decisions• Interconnecting decision E• Routing decisions R• Bilateral settlements f
Source
Destination Zero-DollarPeering
Customer-Provider Settlements
Provider ISP
Customer ISP Customer ISP
Settlement f affects E, R
Multilateral settlements j
j(E,R)$$$
$$
$$
Local decisions: Ei,Ri
Ei
Ri
Given: j
Objective: to maximize ji(E,R)
Our solution: The Shapley Mechanism jEach ISP’s local interconnecting and routing decisions.
x22/4
x72/4
x42/8 x5
2/8
x12/16
x82/16
Route TopologyResults: Routing Incentive
Cost | Profit
Local Min Cost
1
Hot Potato
j
1/4
3/4
1/2
1/2
Global Min Cost
Recall the inefficiency situation
Shapley mechanism distributes 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
• 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.
Results: Incentives for using Optimal Routes
Surprising! Local selfish behaviors coincide with global optimal solution!
x22/4
x72/4
x42/8 x5
2/8
x12/16
x82/16
Route TopologyResults: Interconnecting Incentive
Cost | Profit j
1/2
1/2
Global Min Cost
x62/16
7/12
5/12
x32/16
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
Profit increase
Further the right local ISP connects to the upper backbone ISP.
• 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.
Results: Incentive for Interconnecting
Micro perspective ISP settlement: result summarySelfishly interconnect and route
Route Topology Cost | Profit Connectivity
Global Min Cost
well-connected
Route Topology Cost | Profit Connectivity
Global Min Cost
Balkanized
Route Topology Cost | Profit Connectivity
Hot Potato
Balkanized
ISPs have incentive to interconnect
ISPs have incentive to use optimal routes
j
j
j solves the selfish interconnecting problem
j solves the selfish routing problem
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
• Guideline for – ISPs: negotiate stable and incentive settlements.– Governments: make regulatory policy for the industry.
New Application and Properties of the Shapley Value
Shapley Value: Contributions to Coalitions
Efficiency Symmetry Fairness
Myerson 1977
Efficiency Symmetry Dummy Additivity
Shapley 1953
Efficiency Symmetry Strong Monotonicity
Young 1985
ISP Routing Incentive
ISP Interconnecting Incentive
Ma et al. 2007
ISP Profit Sharing
Ma et al. 2008
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
p
j( )=2.4/6=0.4Empty
S( , p )
Empty
1N! ∈
∑ Di (S(,i))ji =
D (S(p, ))
v( )=0
v( )=0.2v( )-
v( )-v( )=0.8
v( )=0
v( )-v( )=0.8
v( )=0.6v( )-
N: total # of ISPs, e.g. N=3P: set of N! orderings
S(p,i): set of ISPs in front of ISP i
The Shapley value mechanism j