2. Game Theory and Pricing of Internet Services Jean Walrand http://www.eecs.berkeley.edu/~wlr http://www.eecs.berkeley.edu/~wlr (with Linhai He & John Musacchio)

3. Jean Walrand – MIT, January 27, 2005 3 Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions References TOC

4. Jean Walrand – MIT, January 27, 2005 4 Game Theory and Pricing of Internet Services Motivation  Motivation Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions References TOC

5. Jean Walrand – MIT, January 27, 2005 5 Motivation Some users would pay for better network services  Fast occasional transfers (sync. databases, backups, …)  Videoconferences  Streaming of presentations These services are not available A large fraction of infrastructure is poorly used: Wi-Fi access points Why? TOC TOC - Motivation

6. Jean Walrand – MIT, January 27, 2005 6 Motivation (continued) Bandwidth? QoS Mechanisms? Protocols for requesting/provisioning services? Economic Incentives for providing services are lacking TOC TOC – Motivation 

7. Jean Walrand – MIT, January 27, 2005 7 Motivation (continued) Needed: Economic incentives  Billing Mechanism  Fair Revenue Sharing among Providers  Scalable  Correct Incentives Discourage cheating Promote upgrades Revenues Service Quality increases improve TOC TOC  Motivation

8. Jean Walrand – MIT, January 27, 2005 8 Game Theory and Pricing of Internet Services Motivation Three Problems  Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions References TOC

9. Jean Walrand – MIT, January 27, 2005 9 Three Problems 1. Service Differentiation  Market segmentation  Capture willingness to pay more for better services TOC TOC – Three Problems 

10. Jean Walrand – MIT, January 27, 2005 10 Three Problems (cont.) 2. Multiprovider Network Incentives for better services through all providers  Improved Services & Revenues TOC TOC – Three Problems 

11. Jean Walrand – MIT, January 27, 2005 11 Three Problems (cont.) 3. Wi-Fi Access Incentives to open private Wi-Fi access points  Ubiquitous Access TOC TOC  Three Problems

12. Jean Walrand – MIT, January 27, 2005 12 Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation  Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions References TOC

13. Jean Walrand – MIT, January 27, 2005 13 Service Differentiation Model Examples Proposal Joint work with Linhai He TOC TOC – Service Differentiation

14. Jean Walrand – MIT, January 27, 2005 14 Service Differentiation Model  Model Examples Proposal Joint work with Linhai He TOC TOC – Service Differentiation

15. Jean Walrand – MIT, January 27, 2005 15 Model 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 one will happen? p1p1 p2p2 Users A B H L TOC TOC – Service Differentiation – Model Service Differentiation Each user chooses the service class i that maximizes his/her net benefit

16. Jean Walrand – MIT, January 27, 2005 16 Model (cont) p1p1 p2p2 A B H L HL B H L A f 1 (T 0 ) – p 2 f 1 (T 1 ) – p 1 f 1 (T 2 ) – p 2 f 1 (T 0 ) – p 1 A’s benefit T 1 < T 0 < T 2 f i (.) nonincreasing TOC TOC – Service Differentiation  ModelService Differentiation B’s benefit f 2 (T 0 ) – p 1 f 2 (T 2 ) – p 2 f 2 (T 1 ) – p 1 f 2 (T 0 ) – p 2

17. Jean Walrand – MIT, January 27, 2005 17 Service Differentiation Model Examples  Examples Proposal Joint work with Linhai He TOC TOC – Service Differentiation

18. Jean Walrand – MIT, January 27, 2005 18 Example 1 HL H L B A 9 – 4 = 5 9 – 1 = 8 14 – 4 = 10 5 – 1 = 4 14 – 4 = 10 p1p1 p2p2 A B H L f(T 1 ) = 14 f(T 0 ) = 9 f(T 2 ) = 5 p 1 = 4 p 2 = 1 TOC TOC – Service Differentiation – Examples Service Differentiation Here, f i (.) = f(.)

19. Jean Walrand – MIT, January 27, 2005 19 Example 1 HL H L B A 5555 8888 10 4 10 NE TOC TOC – Service Differentiation – Examples Service Differentiation Assume A picks H. Should B choose H or L? Assume A picks H. Should B choose H or L? Assume A picks H. B should choose H. Assume A picks H. B should choose H. Assume A picks L. Should B choose H or L? Assume A picks L. Should B choose H or L? Assume A picks L. B should choose H. Assume A picks L. B should choose H. B  H. Since B chooses H, A should also choose H. NE = Nash Equilibrium

20. Jean Walrand – MIT, January 27, 2005 20 Example 1 HL H L B A NE TOC TOC – Service Differentiation – Examples Service Differentiation A and B choose H, get rewards equal to 5. If they had both chosen L, their rewards would have been 8! A and B choose H, get rewards equal to 5. If they had both chosen L, their rewards would have been 8! Prisoner’s Dilemma! 5555 8888 10 4 10

21. Jean Walrand – MIT, January 27, 2005 21 Example 2 HL H L B A 9 – 4 9 - 4 9 – 1 9 - 1 13 – 4 5 - 1 7 – 1 11 - 4 p1p1 p2p2 A B H L T 1 : 13, 11 T 0 : 9, 9 T 2 : 7, 5 p 1 = 4 p 2 = 1 No Pure Equilibrium f 0 f 1 TOC TOC – Service Differentiation – Examples Service Differentiation

22. Jean Walrand – MIT, January 27, 2005 22 Example 3 Extension to many users Equilibrium exists if 9  0 s.t. willingness to pay total load in class i TOC TOC – Service Differentiation  ExamplesService Differentiation (Indeed, ) Also, the other users prefer L. Note: T 1 and T 2 depend on the split of customers. In this equilibrium, users with prefer H.

23. Jean Walrand – MIT, January 27, 2005 23 Example 3 Analysis of equilibriums: inefficient equilibrium unstable equilibrium Here, f is a concave function and strict-priority scheduling is used. TOC TOC – Service Differentiation  ExamplesService Differentiation  p1-p2p1-p2 f(T 1 )-f(T 2 )

24. Jean Walrand – MIT, January 27, 2005 24 Service Differentiation Model Examples Proposal  Proposal Joint work with Linhai He TOC TOC – Service Differentiation

25. Jean Walrand – MIT, January 27, 2005 25 Proposal Dynamic Pricing Fixed delay + dynamic price Provider chooses target delays for both classes Adjust prices based on demand to guarantee the delays Users still choose the class which maximizes their net benefit TOC TOC – Service Differentiation – Proposal Service Differentiation

26. Jean Walrand – MIT, January 27, 2005 26 Proposal Recommendation: 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 TOC TOC  Service Differentiation – ProposalService Differentiation

27. Jean Walrand – MIT, January 27, 2005 27 Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation Multiprovider Network  Multiprovider Network Wi-Fi Pricing Conclusions References TOC

28. Jean Walrand – MIT, January 27, 2005 28 Multiprovider Network Model Nash Game Revenue Sharing Joint work with Linhai He TOC TOC – Multiprovider Network

29. Jean Walrand – MIT, January 27, 2005 29 Multiprovider Network Model  Model Nash Game Revenue Sharing Joint work with Linhai He TOC TOC – Multiprovider Network

30. Jean Walrand – MIT, January 27, 2005 30 Model + p 1 + p 2 p1+ p2p1+ p2 Monitor marks and processes inter- network billing info Pricing per packet TOC TOC – Multiprovider Network  ModelMultiprovider Network

31. Jean Walrand – MIT, January 27, 2005 31 Multiprovider Network Model Nash Game  Nash Game Revenue Sharing Joint work with Linhai He TOC TOC – Multiprovider Network

32. Jean Walrand – MIT, January 27, 2005 32 Nash Game: Formulation 12 p1p1 p2p2 D Demand = d(p 1 +p 2 ) C1C1 C2C2 A game between two providers Different solution concepts may apply, depend on actual implementation Nash game mostly suited for large networks Provider 1 Provider 2 TOC TOC – Multiprovider Network – Nash Game Multiprovider Network

33. Jean Walrand – MIT, January 27, 2005 33 Nash Game: Result 1. Bottleneck providers get more share of revenue than others 2. Bottleneck providers may not have incentive to upgrade 3. Efficiency decreases quickly as network size gets larger (revenues/provider drop with size) TOC TOC – Multiprovider Network  Nash GameMultiprovider Network

34. Jean Walrand – MIT, January 27, 2005 34 Multiprovider Network Model Nash Game Revenue Sharing  Revenue Sharing Joint work with Linhai He TOC TOC – Multiprovider Network

35. Jean Walrand – MIT, January 27, 2005 35 Revenue Sharing Improving the game Model Optimal Prices Example TOC TOC – Multiprovider Network – Revenue SharingMultiprovider Network

36. Jean Walrand – MIT, January 27, 2005 36 Revenue Sharing Improving the game  Improving the game Model Optimal Prices Example TOC TOC – Multiprovider Network – Revenue SharingMultiprovider Network

37. Jean Walrand – MIT, January 27, 2005 37 Revenue Sharing - Improving the Game Possible Alternatives  Centralized allocation  Cooperative games  Mechanism design Our approach: design a protocol which  overcomes drawbacks of non-cooperative pricing  is in providers’ best interest to follow  is suitable for scalable implementation TOC TOC – Multiprovider Network – Revenue Sharing  ImprovingMultiprovider Network Revenue Sharing

38. Jean Walrand – MIT, January 27, 2005 38 Revenue Sharing Improving the game Model  Model Optimal Prices Example TOC TOC – Multiprovider Network – Revenue SharingMultiprovider Network

39. Jean Walrand – MIT, January 27, 2005 39 Revenue Sharing - Model Providers agree to share the revenue equally, but still choose their prices independently 1 2 p1p1 p2p2 D Demand = d(p 1 +p 2 ) C1C1 C2C2 Provider 1 Provider 2 TOC TOC – Multiprovider Network – Revenue Sharing  ModelMultiprovider Network Revenue Sharing

40. Jean Walrand – MIT, January 27, 2005 40 Revenue Sharing Improving the game Model Optimal Prices  Optimal Prices Example TOC TOC – Multiprovider Network – Revenue SharingMultiprovider Network

41. Jean Walrand – MIT, January 27, 2005 41 Revenue Sharing - Optimal Prices # of providers Lagrange multiplier on link i “locally optimal” total price for the route sum of prices charged by other providers  A system of equations on prices TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing

42. Jean Walrand – MIT, January 27, 2005 42 Revenue Sharing - Optimal Prices (cont.) For any feasible set of  i, there is a unique solution:  On the link i with the largest ,  * ), p i * = N  * + g( p i * )  On all other links, p j * = 0  Only the most congested link on a route sets its total price TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing

43. Jean Walrand – MIT, January 27, 2005 43 Revenue Sharing - Optimal Prices (cont.) {i}{i} {pi*}{pi*} {dr*}{dr*}  a Nash game with  i as the strategy It can be shown that a Nash equilibrium exists in this game. Each provider solves its  i based on local constraints TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing

44. Jean Walrand – MIT, January 27, 2005 44 Revenue Sharing - Optimal Prices (cont.) Comparison with social welfare maximization (TCP) Social: Sharing: Incentive to upgrade  Upgrade will always increase bottleneck providers’ revenue  A tradeoff between efficiency and fairness TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing

45. Jean Walrand – MIT, January 27, 2005 45 Revenue Sharing - Optimal Prices (cont.) Efficient when capacities are adequate  It is the same as that in centralized allocation  Revenue per provider strictly dominates that in Nash game TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing

46. Jean Walrand – MIT, January 27, 2005 46 Revenue Sharing - Optimal Prices (cont.) A local algorithm for computing  i that can be shown to converge to Nash equilibrium: TOC TOC – Multiprovider Network – Revenue Sharing – Optimal Multiprovider Network Revenue Sharing

47. Jean Walrand – MIT, January 27, 2005 47 Revenue Sharing - Optimal Prices (cont.) 1 i d hop count N r =0 congestion price  r =0 flows on route r N r =N r +1  r = max(  r,  i ) A possible scheme for distributed implementation … … … No state info needs to be kept by transit providers. TOC TOC – Multiprovider Network – Revenue Sharing  OptimalMultiprovider Network Revenue Sharing

48. Jean Walrand – MIT, January 27, 2005 48 Revenue Sharing Improving the game Model Optimal Prices Example  Example TOC TOC – Multiprovider Network – Revenue SharingMultiprovider Network

49. Jean Walrand – MIT, January 27, 2005 49 Example C 1 =2 C 2 =5 C 3 =3 demand = 10 exp(-p 2 ) on all routes r1r1 r2r2 r3r3 r4r4 ii link 1 link 3 link 2 prices p2p2 p3p3 p1p1 p4p4 TOC TOC  Multiprovider Network – Revenue Sharing – ExampleMultiprovider Network Revenue Sharing

50. Jean Walrand – MIT, January 27, 2005 50 Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing  Wi-Fi Pricing Conclusions References TOC

51. Jean Walrand – MIT, January 27, 2005 51 Wi-Fi Pricing Motivation Web-Browsing File Transfer TOC TOC – Wi-Fi Pricing Joint work with John Musacchio

52. Jean Walrand – MIT, January 27, 2005 52 Wi-Fi Pricing Motivation  Motivation Web-Browsing File Transfer TOC TOC – Wi-Fi Pricing Joint work with John Musacchio

53. Jean Walrand – MIT, January 27, 2005 53 Motivation Path to Universal WiFi Access  Massive Deployment of 802.11 base stations for private LANs  Payment scheme might incentivize base station owners to allow public access. Direct Payments  Avoid third party involvement.  Transactions need to be “self enforcing” Payments:  Pay as you go: In time slot n, - Base Station proposes price p n - Client either accepts or walks away  What are good strategies? TOC TOC – Wi-Fi Pricing  MotivationWi-Fi Pricing

54. Jean Walrand – MIT, January 27, 2005 54 Wi-Fi Pricing Motivation Web-Browsing  Web-Browsing File Transfer TOC TOC – Wi-Fi Pricing Joint work with John Musacchio

55. Jean Walrand – MIT, January 27, 2005 55 Web Browsing Client Utility U = Utility per unit time K = Intended duration of connection Random variable in [0, 1] Known to client, not to BS Random variable in {1, 2, …} Known to client, not to BS BS Utility p 1 + p 2 + … + p N U.min{K, N} N = duration TOC TOC – Wi-Fi Pricing – Web Browsing Wi-Fi Pricing

56. Jean Walrand – MIT, January 27, 2005 56 Web Browsing Theorem Perfect Bayesian Equilibrium: Client accepts to pay p as long as p ≤ U BS chooses p n = p* = arg max p p P(U ≥ p) Note: Surprising because BS learns about U … TOC TOC – Wi-Fi Pricing  Web BrowsingWi-Fi Pricing

57. Jean Walrand – MIT, January 27, 2005 57 Wi-Fi Pricing Motivation Web-Browsing File Transfer  File Transfer TOC TOC – Wi-Fi Pricing Joint work with John Musacchio

58. Jean Walrand – MIT, January 27, 2005 58 File Transfer Client Utility K.1{K ≤ N} BS Utility p 1 + p 2 + … + p N K = Intended duration of connection Random variable in {1, 2, …} Known to client, not to BS N = duration TOC TOC – Wi-Fi Pricing – File Transfer Wi-Fi Pricing

59. Jean Walrand – MIT, January 27, 2005 59 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 …. TOC TOC – Wi-Fi Pricing – File Transfer Wi-Fi Pricing

60. Jean Walrand – MIT, January 27, 2005 60 Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions  Conclusions References TOC

61. Jean Walrand – MIT, January 27, 2005 61 Conclusions Dynamic Pricing to adjust QoS Cooperative pricing -> distributed algorithm Web browsing -> constant price File transfer -> one-time price TOC TOC – Conclusions 

62. Jean Walrand – MIT, January 27, 2005 62 Conclusions Basic objective Improve revenues by better mechanisms for - service differentiation - pricing - revenue sharing Some preliminary ideas New pricing schemes - rational (equilibrium) - desirable incentives - implementable (scalable protocols) TOC TOC  Conclusions

63. Jean Walrand – MIT, January 27, 2005 63 Game Theory and Pricing of Internet Services Motivation Three Problems Service Differentiation Multiprovider Network Wi-Fi Pricing Conclusions References  References TOC

64. Jean Walrand – MIT, January 27, 2005 64 References TOC TOC  References Linhai He and Jean Walrand, "Pricing Differentiated Internet Services," INFOCOM 2005 Linhai He and Jean Walrand, "Pricing and Revenue Sharing Strategies for Internet Service Providers," INFOCOM 2005 John Musacchio and Jean Walrand, "Game-Theoretic Analysis of Wi-Fi Pricing," IEEE Trans. Networking, 2005

65. Jean Walrand – MIT, January 27, 2005 65 Thank you!