Economic Models of Networks

Transcription

1 Economic Models of Networks Jean Walrand Collaborators: Shyam Parekh EECS U.C. Berkeley John Musacchio Pravin Varaiya Venkat Anantharam Galina Schwartz Libin Jiang

2 Economic Models of Networks Motivation Issues Basic Effects Services Neutrality Peering Security Conclusions References TOC Motivation Issues Effects Services Neutrality Peering Security Conclusions References

3 Economic Models of Networks Motivation Issues Basic Effects Services Neutrality Peering Security Conclusions References TOC Motivation Issues Effects Services Neutrality Peering Security Conclusions References

4 Motivation

5 Motivation Why? (Why not leave this to economists?) Technology (e.g., protocols) affects markets Economics (e.g., ROI) drives deployment Economics o cs should guide designs s Examples: Skype changes economics of phone network and of Internet Lack of economic incentives absence of QoS, poor security Protocol for choice & pricing might change Internet Neutrality decisions affect investment incentives

6 Economic Models of Networks Motivation Issues Basic Effects Services Neutrality Peering Security Conclusions References TOC Motivation Issues Effects Services Neutrality Peering Security Conclusions References

7 Issues Services differentiation, upgrades, choice, contracts Investments incentives, free-riding Pi Pricing i discrimination, competition

8 Economic Models of Networks Motivation Issues Basic Effects Services Neutrality Peering Security Conclusions References TOC Motivation Issues Effects Services Neutrality Peering Security Conclusions References

9 Basic Effects Network Externality Castles-on-the-Rhine Tragedy of the Commons Free-Riding Uncertainty Repeated Game

10 Basic Effects Network Externality Castles-on-the-Rhine Tragedy of the Commons Free-Riding Uncertainty Repeated Game

11 Network Externality Unlike other goods or services, networks have a utility that depends on the number of users. Positive Externality: More users Network more valuable for each user Negative Externality: More users Congestion disutility Model: User utility U(N) = A(N) C(N) p A(N) = positive utility C(N) = congestion disutility p = price

12 Network Externality U(N) = A(N) C(N) p User joins if U(N) > 0. For a fixed price p, if N > N 0 (p), N N 1 (p). 1(p) In fact, C(N) depends on investment level. As investment x increases, C(N, x) decreases and N 1 (p, x) increases. Thus, one has the net revenue for the operator Max p pn 1 (p, x) ax where ax is the opportunity cost. The operator maximizes over x.

13 Network Externality Note the advantage of connecting networks. Let s ignore C(N): Networks with N 1 and dn 2 users get connected N 1 + N 2 users Value becomes (N 1 + N 2 )A(N 1 + N 2 ) instead of N 1 A(N 1 ) + N 2 A(N 2 ) This effect justifies the value of peering (see later).

14 Basic Effects Network Externality Castles-on-the-Rhine Tragedy of the Commons Free-Riding Uncertainty Repeated Game

15 Castles-on-the-Rhine Selfish providers overcharge: They neglect their impact on others.

16 Castles-on-the-Rhine Selfish providers overproduce: They neglect their impact on others.

17 Basic Effects Network Externality Castles-on-the-Rhine Tragedy of the Commons Free-Riding Uncertainty Repeated Game

18 Tragedy of the Commons: Intro Slope = 1 Slope = n Selfish Social planner Selfish users over-consume: They neglect their impact on others.

19 Tragedy of the Commons: Pricing

20 Tragedy of the Commons: Pricing 2

21 Tragedy of the Commons: Pricing 2

22 Tragedy of the Commons: Pricing 3 d(p(x)) (X)) X N µx

23 Basic Effects Network Externality Castles-on-the-Rhine Tragedy of the Commons Free-Riding Uncertainty Repeated Game

24 Free-Riding Free-Riding = benefiting from others investment

25 Free-Riding

26 Free-Riding

27 Basic Effects Network Externality Castles-on-the-Rhine Tragedy of the Commons Free-Riding Uncertainty Repeated Game

28 Uncertainty Uncertainty generally causes under-investment and inefficiency

29 Uncertainty Uncertainty may cause missing markets

30 Basic Effects Network Externality Castles-on-the-Rhine Tragedy of the Commons Free-Riding Uncertainty Repeated Game

31 Repeated Game: Folk s Theorem In repeated games, almost anything goes.

32 Repeated Game: Folk s Theorem

33 Economic Models of Networks Motivation Issues Basic Effects Services Neutrality Peering Security Conclusions References TOC Motivation Issues Effects Services Neutrality Peering Security Conclusions References

34 Economic Models of Networks Motivation Issues Basic Effects Services Neutrality Peering Security Conclusions References TOC Motivation Issues Effects Services Neutrality Peering Security Conclusions References

35 Services Service Differentiation Pricing Upgrades Service Choice

36 Services Service Differentiation Pricing Upgrades Service Choice

37 Service Differentiation 1kByte/s 2000 minutes/month 10kByte/s 400 minutes/month URGENT REAL TIME BEST EFFORT M H L Priority

38 Service Differentiation

39 Services Service Differentiation Pricing Upgrades Service Choice

40 Pricing: Paris Metro

41 Pricing: Paris Metro

42 Pricing: Paris Metro

43 Review of Part 1 Prices, Investments Technology, Performance Evaluation Demand Network Services Incentives, Strategies,

44 Review of Part 1 Example: Paris Metro Pricing $20/month $5/month Network Network Great QoS Poor QoS Demand Poor QoS 08C 0.8C Great QoS 5 20 QoS: G if L < 0.2C 0.2C Price

45 Review of Part 1 Users and Providers interact in a network In general, Selfish optimal Social optimal (price of anarchy) Selfish users over-consume Selfish providers over-price, under-invest Internalize the externality Congestion pricing Revenue-sharing agreement

46 Services Service Differentiation Pricing Upgrades Service Choice

47 Pricing: Wi-Fi Service

48 Pricing: Wi-Fi Service Web Browsing Client Utility U.min{K, N} N=duration BS Utility U = Utility per unit time Random variable in [0, 1] Known to client, not to BS K = Intended duration of connection Random variable in {1, 2, } Known to client, not to BS p 1 + p p N

49 Pricing: Wi-Fi Service Web Browsing Theorem Perfect Bayesian Equilibrium: Client accepts to pay p n as long as p n U leaves as soon as p n > U BS chooses p n =p* = arg max p p P(U p) Notes: Surprising because BS learns about U Loss of revenues: E(U)/p*1{U p*} [e.g., unif. [0, 1] Loss = 2]

50 Pricing: Wi-Fi Service File Transfer Client Utility BS Utility K.1{K N} K = Intended duration of connection Random variable in {1, 2, } Known to client, not to BS N = duration p 1 + p p N

51 Pricing: Wi-Fi Service File Transfer Theorem Perfect Bayesian Equilibrium: Client accepts to pay 0 at time n < K p K at time n = K BS chooses a one-time-only payment pay n* at time n* = arg max n np(k = n) Note: True for bounded K. Proof by backward induction. Unfortunate.

52 Pricing: Auction Second Price

53 Pricing: Auction - VCG

54 Pricing: Auction - VCG

55 Pricing: Auction - VCG

56 Pricing: Auction Bidding for QoS g c 0, ,7 10 0,4 10 c = 1 c=2 c = 3 0,2 c = 4 02 Max. # connections

57 Pricing: Auction Bidding for QoS

58 Pricing: Prisoner s Dilemma Users A B H L p 1 p 2 Priority Each user chooses the service class i that maximizes his/her net benefit Two possible outcomes: 1. Users occupy different queues (delays = T 1 & T 2 ) 2. Users share the same queue (delay = T 0 ) If users do not randomize their choices, which outcome will happen?

59 Pricing: Prisoner s Dilemma B s benefit A s benefit B A H H L p 1 A H T 1 <T 0 <T 2 B L p 2 f i (.) nonincreasing f 1 (T 0 ) p 1 f 1 (T 1 ) p 1 f (T ) p f 2 (T 2 ) p 2 f 1 (T 2 ) p 2 f 1 (T 0 ) p 2 f 2 (T 1 ) p 1 f 2 (T 0 ) p 2 L

60 Pricing: Prisoner s Dilemma Ex. 1 A A H p f(t 1 1) = 14 p 1 = 4 p f(t )= B L p 2 = 1 f(t 2 ) = 5 B H L f i ()=f() (.) f(.) H NE 9 4 = = = = 4 L 5 1 = = =10 9 1=8

61 Pricing: Prisoner s Dilemma Ex. 2 A f 0 f 1 A H p 1 T : 13, 11 p 1 = 4 B L 1 p 2 T 0 : 9, 9 p 2 = 1 B T 2 : 7, 5 H H 2, L L ilibrium No Pur re Equ

62 Pricing: Prisoner s Dilemma Ex. 3 willingness to pay Equilibrium exists if θ 0 s.t. total load in class i Also, the other users prefer L. Note: T 1 and T 2 depend on the split of customers.

63 Pricing: Prisoner s Dilemma Ex. 3 θ(f(t 1 )-f(t 2 )) unstable equilibrium p 1 -p 2 inefficient equilibrium θ

64 Pricing: Prisoner s Dilemma Proposal Dynamic Pricing Fixed delay + dynamic price Provider chooses target t delays for both classes Adjust prices based on demand to guarantee the delays Users still choose the class which maximizes their net benefit

65 Proposal Dynamic Pricing (cont) Why is it better? A Nash equilibrium exists This equilibrium approximates the outcome of a Vickrey auction If an arbitrator knows f i (T 1 ) and f i (T 2 ) from all users, Vickrey auction leads to socially efficient allocation Approximation becomes exact when many users Simpler to implement

66 Services Service Differentiation Pricing Upgrades Service Choice

67 Upgrades

68 Upgrades $ $ Provider 1 Provider 2

69 Upgrades Both Provider s Revenues Increase a $ $ $ f $ Users less dissatisfied Provider 1 Provider 2 Provider 1 invests U to upgrade.

70 Upgrades Both Provider s Revenues Increase R $ $ R $ $ Users more satisfied Provider 1 Provider 2 Provider 2 invests $U to upgrade.

71 Upgrades Then an SPE is: Upgrade Immediately Both providers choose to upgrade in the current period If also Then Upgrade Immediately is a unique SPE by iterated strict dominance The following are also SPE: No First Upgrade No provider willing to upgrade first Delayed Upgrade Each provider waits until period n to upgrade Mixed Upgrade Each provider upgrades with probability α in each period.

72 Upgrades If also Then an SPE is: Never upgrade Do not upgrade no matter what Asymmetric Freeride One player upgrades the other freerides Mixed Freeride Players upgrade with probability α, until one upgrades. Then other one freerides

73 Services Service Differentiation Pricing Upgrades Service Choice

74 Choice Idea: Users offered real-time choice: red and blue red and blue not specified to users in detail; Users decide based on which they think gives better performance Market will push providers to make improvements, and offer services more suitable for intensive real-time applications. No need to dictate QoS parameters a standard. Let the market decide!

75 Economic Models of Networks Motivation Issues Basic Effects Services Neutrality Peering Security Conclusions References TOC Motivation Issues Effects Services Neutrality Peering Security Conclusions References

76 Neutrality Issues Model Preliminary Results Details

77 Neutrality Issues Model Preliminary Results Details.

78 Issues Contentious Debate But, what (if any) bearing should the issues have on the future network architecture? Does future architecture need features for Revenue sharing between content and transit providers?

79 Issues Content Provider A $ $ $??? Content Provider B $ ISP 1 ISP 2 ISP 2 needs to invest To enable A s service

80 Issues A $ $ $??? Should A have to pay ISP 2? B ISP 1 ISP 2 $ Content providers pay their ISP Would allowing 2 to charge A encourage 2 to invest? discourage A to invest? What revenue sharing mechanisms should new Internet t have?

81 Neutrality Issues Model Preliminary Results Details.

82 Model (Content Investment, ISP Investment) Usage Usage (Ad Revenue to Content, User Revenue to ISPs) ISP NEUTRAL NOT NEUTRAL Each Chooses: Investment level User Price Investment level User Price Price for each content provider Content Prov. Each Chooses Investment level

83 Neutrality Issues Model Preliminary Results Details.

84 Preliminary Results Elasticity of User Demand Low High Ad dvertis ing Rates Low High Neutral Better Non-Neutral Better

85 Neutrality Issues Model Preliminary Results Details.

86 Details. Clicks for C 1

87 Details. Non-Neutral: Neutral: Neutral:

88 Details.

89 Details. V = 0.5 and w = Graphs are for N = 1 to 10 (bottom to top) X-axis is a/θ

90 Security Today Market for Security

91 Security Today Market for Security

92 Today ANALOGY Zzzz Users do not bear full cost of poor computer maintenance Drivers do not bear full cost of reckless driving. Liability insurance incentivizes drivers to be careful.

93 Security Today Market for Security

94 Market Example: Users pay to be certified by a Certification Agency (CA) $ CA takes on liability for attacks traced back to user Zzzz CA incentivized to encourage users to take due care OS Update Antivirus Update

95 Market Possible incentives for users to go to CA Network drops discards uncertified packets in crisis. Adverse selection a problem Make insurance mandatory? Architectural Requirements: Improve traceability of attacks Mechanism for dropping uncertified packets

96 Economic Models of Networks Motivation Issues Basic Effects Services Neutrality Peering Security Conclusions References TOC Motivation Issues Effects Services Neutrality Peering Security Conclusions References

97 Conclusions Users Choice Economics Essential, but less developed! Prices Utility Network Devices Physics Measure Algorithms Control

98 Economic Models of Networks Motivation Issues Basic Effects Services Neutrality Peering Security Conclusions References TOC Motivation Issues Effects Services Neutrality Peering Security Conclusions References

99 References Here is a list of some references I used to prepare the material.. George Akerlof, The Market for Lemons PioBaake, ThorstenWichmann-On the Economics of Internet Peering -January Chiu D-M and Jain R (1989). Analysis of the increase and decrease algorithms for congestion avoidance in computer networks.comp Networks and ISDN Sys 17: 1±14. Courcoubetis, C and R.R. Weber(2003). Pricing Network Services, Springer Verlag. Cremer, J., P. Rey& J. Tirole,"Connectivity in the Commercial Internet" Journal of Industrial Economics, December 2000,vol48, n 4, pp Feigenbaum, C. H. Papadimitriou, R. Sami, S. Shenker(2002) A BGP-based Mechanism for Lowestcost Routing,"in Proceedings of the 21st Symposium on Principles of Distributed Computing, ACM Press, New York, 2002, pp Fudenberg, D. and J. Tirole(1991). Game Theory. MIT Press. Geoff Huston Interconnection and Peering, November Garrett Hardin, The Tragedy of the Commons, 1968 P. Honeyman, G. Schwartz, Interdependence of Reliability and Security, Workshop on Economics of Information Security, CMU, June 2007 ITS, Congestion Pricing J. Musacchio, S. Wu, A Game Theoretic Model for Network Upgrade Decisions, Allerton Conference 2006.

100 References J. Musacchio, S. Wu, The Price of Anarchy in a Network Pricing Game, in submission. Musacchio, J. and J. Walrand. Game-theoretic analysis of Wi-FiAccess Pricing, in preparation. J. Musacchio, J. Walrand, Economic Consequences of Weak Network Neutrality, to appear at Asilomar Tim Roughgarden, Selfish Routing and the Price of Anarchy Hal Varian, System Reliability and Free Riding, 2001 Y. Jin and G. Kesidis, Feasible pricing of differentiated services for the emerging Internet, in Proc. 40th AllertonConference on Communications, Control and Computing, Oct J.-J. J Laffont, S. Marcus, P. Rey, and J. Tirole, Internet t t interconnection ti and the off-net-cost t pricing i principle, Andrew Odlyzko,Paris Metro Pricing for the Internet(1998),ACM Conference on Electronic Commerce [PG93] AbhayK. Parekh, Robert G. Gallager: A Generalized Processor Sharing Approach to Flow Control in Integrated t Services Networks: The Multiple l Node Case. INFOCOM 1993: [S90] Vernon Smith et al., Auction Design for Composite Goods, Journal of Economic Behavior and Organization, 14 (1990) [SV03] Jun Shu and PravinVaraiya, Pricing Network Services.Infocom2003. [V61] Vickrey, W.,1961, Counterspeculation, Auctions, and Competitive Sealed Tenders, Journal of Finance, XVI, 8-37.