The Shapley Value: Its Use and Implications on Internet Economics

Transcription

1 The Shapley Value: Its Use and Implications on Internet Economics Prof. John C.S. Lui Choh-Ming Li Chair Professor Computer Science & Engineering Department The Chinese University of Hong Kong Collaborate with RTB Ma (NUS), V. Misra & D. Rubenstein (Columbia Univ.)

2 Outline Network economics research and problems Two problems Design an efficient and fair profit-sharing mechanism for cooperative s Encourage selfish s to operate at global efficient/optimal points

3 Building blocks of the Internet: s The Internet is operated by thousands of interconnected Internet Service Providers (s). An is an autonomous business entity. Provide Internet services. Common objective: to make profit.

4 Oscar Wilde, British poet ( ): When I was young, I thought money was the most important thing. Now that I am old,. I know it is the most important thing.

5 Three types of s 1. Eyeball (local) s: Provide Internet access to residential users. E.g. Time Warner Cable, Comcast, SingNet, MobileOne, Hutchinson 2. Content s: Server content providers and upload information. E.g. Cogent, Akamai (Content Distribution Networks) 3. Transit s: Provide global connectivity, transit services for other s. E.g. Tier 1 s: Level3, Qwest, Global Crossing C T B

6 A motivating example Win-win under Client-Server: Content providers find customers Users obtain the content s generate revenue B 50/month C B 50/month Fixed-rate charge 5/Gb Volume-based charge B 50/month

7 What happens with P2P traffic? Win-lose under P2P paradigm: Content providers pay less Customers get faster downloads Content obtains less revenue Eyeball s handle more traffic B 50/month C B 50/month 5/Gb B 50/month In reality: P2P is a nightmare for s.

8 Engineering solutions and beyond Proposed engineering approaches: s: Drop P2P packets based on port number Users: Dynamic port selection s: Deep packet inspection (DPI) Users: Disguise by encryption s: Behavioral analysis A new/global angle: Network Economics Goal: a win-win/fair solution for all. Issues: What is a win-win/fair solution? How do we find it? How do we design algorithms/protocols to achieve it? Interdisciplinary research Networking, Economics, Theoretic Computer Science Operations Research, Regulatory Policy

9 Two important issues of the Internet 1. Network Neutrality Debate: Content-based Service Differentiations? B Yes T No Legal/regulatory policy for the Internet industry: Allow or Not? Allow: s might over-charge; Not: s have no incentive to invest. VS. In Oct 2007, Comcast was found to delay and block BitTorrent packets. In Aug 2008, FCC ruled that Comcast broke the law. In Apr 6 th 2010, Federal court ruled that FCC didn t have the authority to censure Comcast for throttling P2P packets.

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12 Two important issues of the Internet 1. Network Neutrality Debate: Content-based Service Differentiations? B Yes T No Legal/regulatory policy for the Internet industry: Allow or Not? Allow: s might over-charge; Not: s have no incentive to invest. Either extreme will suppress the development of the Internet. 2. Network Balkanization: Break-up of connected s 15% of Internet unreachable C T Cogent Level 3 Not a technical/operation problem, but an economic issue of s. Threatens the global connectivity of the Internet.

13 Other important problems that can be looked at B T A new/global angle: Network Economics Goal: a win-win/fair solution Issues: how do we design algorithms/protocols to achieve it? C T

14 Problems we try to solve Problem 1: Find a win-win/fair profit-sharing solution for s. Challenges What s the solution? s don t know, even with best intentions. How do we find it? Complex s structure, computationally expensive. How do we implement it? Need to be implementable for s.

15 How do we share profit? -- the baseline case C 1 B 1 One content and one eyeball Profit V = total revenue = content-side + eyeball-side Win-win/fair profit sharing: ϕ = ϕ = B 1 C V

16 How do we share profit? -- two symmetric eyeball s B 1 Win-win/fair properties: Symmetry: same profit for symmetric eyeball s ϕ = ϕ = ϕ B1 B 2 B Efficiency: summation of individual profits equals V ϕ + 2ϕ = V C1 B Fairness: same mutual contribution for any pair of s Unique solution (Shapley value) C 1 B 2 ϕ 1 V = ϕ 0 C 1 2 B 1 ϕ = 2 C1 3 ϕ = B V 1 6 V

17 Axiomatic characterization of the Shapley value What is the Shapley value? A measure of one s contribution to different coalitions that it participates. Shapley 1953 Myerson 1977 Young 1985 Shapley Value Efficiency Symmetry Dummy Additivity Efficiency Symmetry Fairness Efficiency Symmetry Strong Monotonicity

18 Stability of the Shapley value V({1}) = a, V({2}) = b V({1,2}) = c > a + b. Convex game: V(SUT)>= V(S)+V(T) Whole is bigger than the sum of parts.

19 Stability of the Shapley value V({1}) = a, V({2}) = b V({1,2}) = c > a + b. Convex game: V(SUT)>= V(S)+V(T) Whole is bigger than the sum of parts. Core: the set of efficient profit-share that no coalition can improve upon or block.

20 Stability of the Shapley value V({1}) = a, V({2}) = b V({1,2}) = c > a + b. Convex game: V(SUT)>= V(S)+V(T) Whole is bigger than the sum of parts. Core: the set of efficient profitshare that no coalition can improve upon or block. Shapley [1971] Core is a convex set. The value is located at the center of gravity of the core.

21 How to share profit? -- n symmetric eyeball s B 1 C 1 B 2 B n Theorem: the Shapley profit sharing solution is 1 ϕ = V, ϕ = n B V n(n+1) C n+1

22 Results and implications of profit sharing 1 ϕ = V, ϕ = n B V n(n+1) C n+1 With more eyeball s, the content gets a larger profit share. Multiple eyeball s provide redundancy, The single content has leverage. Content s profit with one less eyeball: C The marginal profit loss of the content : If an eyeball leaves The content will lose 1/n 2 of its profit. If n=1, the content will lose all its profit. ϕ = Δϕ = n-1 V - n V = - 1 C ϕ n n+1 n 2 C 1 B 1 C n-1 V n B n-1 B n

23 Profit share -- multiple eyeball and content s C 1 B 1 C 2 B 2 C m B n Theorem: the Shapley profit sharing solution is m n ϕ = V, ϕ = V B n(n+m) C m(n+m)

24 Results and implications of profit sharing m V ϕ B= n (n+m), ϕ C = n V m(n+m) C 1 B 1 Each s profit share is Inversely proportional to the number of s of the same type. Proportional to the number of s of the other type. C 2 C m B 2 B n Intuition When more s provide the same service, each of them obtains less bargaining power. When fewer s provide the same service, each of them becomes more important.

25 Profit share -- eyeball, transit and content s C 1 T 1 B 1 C 2 T 2 B 2 C m T k B n Theorem: the Shapley profit sharing solution is

26 Profit share general topologies C 1 T 1 Theorem: B 1 B 2 Dynamic Programming! 1 ϕ i = [Σ ϕ i (N \{j}) + V {i is veto} ] N j i 2. Whether the profit can still be generated: C 1 is veto. C 1 T 1 B 1 B 2 1. Shapley values under sub-topologies: ϕ C1 = 0 C 1 T 1 ϕ C1 = 1/3V C 1 T 1 ϕ C1 = 1/3V C 1 T ϕ C1 = [0 + V + V + V] = V B 1 B 2 B 1 B 2 B 1 B 2

27 Current Business Practices: A Macroscopic View Two forms of bilateral settlements: T Zero-Dollar Peering T Provider s Customer-Provider Settlement C Customer s B

28 Achieving the win-win/fair profit share Content-side Revenue Eyeball-side Revenue

29 Achieving the win-win/fair profit share Content-side Revenue Eyeball-side Revenue Two revenue flows to achieve the Shapley profit share: Content-side revenue: Content àtransit àeyeball Eyeball-side revenue: Eyeball àtransit àcontent

30 Achieving the Shapley solution by bilateral settlements Content-side Revenue Customers Providers Customers Eyeball-side Revenue Zero-dollar Peering When CR BR, bilateral implementations: Customer-Provider settlements (Transit s as providers) Zero-dollar Peering settlements (between Transit s) Current settlements can achieve fair profit-share for s.

31 Achieving the Shapley solution by bilateral settlements Customer Provider Eyeball-side Revenue Content-side Revenue Paid Peering 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.

32 Recap: Practices from a Macroscopic View Two current forms of bilateral settlements: Our Implication: Two new forms of bilateral settlements: T Zero-Dollar Peering Paid Peering T Reverse Customer- Provider Settlement Customer-Provider Settlement C B Next, a Microscopic View to inspect on behaviors

33 Problems we try to solve Problem 1: Find a win-win/fair profit-sharing solution for s. Challenges What s the solution? s don t know, even with best intentions. Answer: The Shapley value. How do we find it? Complex structure, computationally expensive. Result: Closed-form solution and Dynamic Programming. How do we implement it? Need to be implementable for s. Implication: Two new bilateral settlements. Problem 2: Encourage s to operate at an efficient/optimal point. Challenges How do we induce good behavior? Selfish behavior may hurt others s. What is the impact on the entire network? Equilibrium is not efficient.

34 Current Business Practices: A Micro Perspective Three levels of decisions Bilateral settlements φ Routing decisions R (via BGP) Interconnecting decision E Provider Settlement φ affects E, R Customer-Provider Settlements Interconnection provider withdrawal over-charges Hot-potato Route change Routing Source Destination Zero-Dollar Peering Customer Shortest Path Routing Customer

35 Our solution: The Shapley Mechanism ϕ Recall: three levels of decisions Bilateral Multilateral settlements φ ϕ Routing decisions R Interconnecting decision E Provider ϕ collects revenue from customers Settlement φ affects E, R ϕ distributes profits to s Customer-Provider Settlements ϕ(e,r) Source Peering Destination Zero-Dollar Customer Customer

36 behaviors under the Shapley mechanism ϕ Profit distribution mechanism: ϕ Local decisions: E i,r i Objective: to maximize ϕ i (E,R) E i R i

37 Results: Incentives for using Optimal Routes Given any fixed interconnecting topology E, s can locally decide routing strategies {R i* } to maximize their profits. Theorem (Incentive for routing): Any i can maximize its profit ϕ i by locally minimizing the global routing cost. Implication: s adapt to global min cost routes. Corollary (Nash Equilibrium): Any global min cost routing decision is a Nash equilibrium for the set of all s. Implication: global min cost routes are stable. Surprising! Local selfish routing behavior coincides with the globally optimal solution!

38 Results: Incentive for Interconnecting For any topology, a global optimal route R * is used by all s. s can locally decide interconnecting strategies {E i* } to maximize their profits. Theorem (Incentive for interconnecting): After interconnecting, s will have non-decreasing profits. Implication: s have incentive to interconnect. Does not mean: All pairs of s should be connected. Redundant links might not reduce routing costs. Sunk cost is not considered. Local selfish interconnecting decisions form a globally optimal topology!

39 Problems we try to solve Problem 1: Find a win-win/fair profit-sharing solution for s. Challenges What s the solution? s don t know, even with the best intention. Answer: The Shapley value How to find it? Complex s structure, computationally expensive. Result: Closed-form sol. and Dynamic Programming How to implement? Need to be implementable for s. Implication: Two new bilateral settlements Problem 2: Encourage s to operate at an efficient/optimal point. Challenges How do we induce good behavior? Selfish behavior hurts other s. Answer: Shapley profit-distribution mechanism Result: Incentives for optimal routes and interconnection What is the impact on the entire network? Equilibrium is not efficient. Result: Globally optimal/efficient equilibrium

40 A Game-theoretic framework Non-cooperative Game Theory Mechanism Design: e.g. Tax Policy, Auction Theory Coalition Game Theory New cooperative applications Data Centers Networks QoS supported services

41 Questions? Thank you very much!