1. Issues in Pricing Internet Services Linhai He & Jean Walrand Dept of EECS, U.C. Berkeley March 8, 2004

2. 2 Challenges Stagnant telecommunication industry “We know how to route packets; what we don’t know how to do is route dollars.” - David Clark, MIT ) Need efficient economic mechanisms to increase the profit of Internet service providers

3. 3 Approach Combine economics with network protocol design –Economics help identify utilities and strategies of users –Protocols are designed to shape and enable the strategies Goal: Networks mutually beneficial to both users and providers Two essential ingredients –More revenues from service differentiation/market segmentation Question: How to price differentiated services? –Fair revenue distribution among the providers Question: How should a provider price its share of service?

4. 4 Outline Pricing Differentiated Services –Motivating examples –Dynamic pricing schemes Pricing with Multiple Providers –Motivations –Non-cooperative pricing –Revenue sharing policy –Implementation Pricing Wireless Access (John Musacchio) Summary and Future Work

5. 5 Pricing Differentiated Services: Base Model p1p1 p2p2 strategic users If users do not randomize their choices, what kind of equilibrium would happen? Users choose the service class which maximizes their net benefit Delay T i : no preset targets; determined by users’ own choices − If equilibrium exists, higher price p ) smaller delay T Congestion externality exists within and between the classes

6. 6 Outcome A. Prisoner’s Dilemma H. P. L. P. H. P. L. P. B A p1p1 p2p2 A B f(T 1 ) = 14 f(T 2 ) = 5 f(T 0 ) = 9 p 1 = 4 p 2 = 1 9-4 = 5 5-1 = 4 14-4 =10 5-1 = 4 9-1 = 8 NE H. P. L. P.

7. 7 Outcome B. No Pure-Strategy Equilibrium H. P.L. P. H. P. L. P. B A p1p1 p2p2 A B p 1 = 4 p 2 = 1 9-4 = 5 7-1 = 6 11-4 = 7 13-4 = 9 5-1 = 4 9-1 = 8 f1f2f1f2 T 1 T 0 T 2 13 9 7 11 9 5

8. 8 General Conditions for Two-Users Case If, both users will choose to use high-price class ) Prisoners’ Dilemma If f a is convex and f b is concave, or vice versa, then no pure-strategy equilibrium exists. H. P.L. P. H. P. L. P. B A

9. 9 Extension to Many-User Case Model –Infinite number of atomic users making independent choices –User’s payoff function willingness to pay; with load density  (  ) Equilibrium load in class i delay in class i leave low-price class high-price class 22 11 0 

10. 10 Properties of Equilibrium: an example Utility function f is concave; strict-priority scheduling 11 p1-p2p1-p2 stable but inefficient equilibrium unstable equilibrium   1 ! x 1 ! search  2 which satisfies

11. 11 Properties of Equilibrium − Perturbation around equilibrium cause change in users’ payoff Stability of the equilibrium If M >0, then users with  2 B(  1,  ) has incentive to switch  unstable This might happen if congestion externality is significant between classes. Multiple equilibria if is not monotonic in  Example: small group of users move from L.P. into H.P. Consider

12. 12 Challenge How to design the system so that it is stable and efficient? Knobs one could turn: –Scheduling policy –Pricing scheme

13. 13 To Stabilize… Scheduling policy: Paris-Metro model [Odlyzko] –Inflexible in adapting to changes in user demand –Possible loss in revenue for being non-work-conserving Pricing Scheme: load-based pricing p i, p i (x i ) –Choose p i (x i ) so that M <0 under perturbation –Resulting equilibrium is stable, if p1p1 p2p2 users No congestion externality between classes ) always stable where k is a bound on

14. 14 user D1D1 D2D2 agent (VCG) bid:  charge: p i To be more efficient… Effect on last user in L.P. Effect on last user in H.P. and L.P. Goal –assignment rule which maximizes the sum of users’ utilities Mechanism-Design approach –Socially efficient ▪ Assign users from H.P. to L.P. according to their bid –Incentive compatible: charge a user by her externality effect

15. 15 Our Solution Congestion pricing Equilibrium p1p1 p2p2 user DiDi pipi Users choose to join H.P. to L.P. in decreasing order of  two marginal users equilibrium prices externality cost of the marginal users

16. 16 Pricing with Multiple Providers: Outline Challenges Model and formulation Non-Cooperative Pricing Revenue Sharing Implementation

17. 17 Challenges Internet is an interconnection of service providers –An Internet service has to be jointly provided by a group of service providers –Providers are neither cooperative nor adversary; they act strategically in their own interests Design requirements on pricing schemes –Fair distribution of revenue –Scalable implementation –Robust against gaming or cheating

18. 18 A Possible Implementation Provider 2 Provider 1 How should each provider price its share of service? request $1 $2 request $1 ACK $3

19. 19 Objectives Formulate an abstract model that summarizes common issues in various implementations Understand how providers would charge for their services when acting strategically Design a pricing mechanism which meets the aforementioned design requirements

20. 20 Model - Users Service Model –QoS requirement ) limits on link load Users’ aggregate demand –May be regulated by price p –Demand d(p) is decreasing and differentiable –Revenue pd(p) has a unique maximizer –For use later, define

21. 21 Model - Providers Local capacity limit is private information QoS requirements and routes are fixed and are independent from prices charge p 1 + p 2 provider 2 Revenue = Price £ Demand Choose price to maximize its own revenue, while regulate the load to meet QoS requirement demand p 1 + p 2 + p 1 provider 1 + p 2

22. 22 Formulation: an example 12 p1p1 p2p2 D demand = d(p 1 +p 2 ) C1C1 C2C2 A pricing game between two providers Different solution concepts may apply, depend on actual implementation Nash game mostly suited for large networks Provider 1 Provider 2

23. 23 Outcome of the Nash Game Essentially a Cournot game with coupled local constraints Bottleneck providers get more share of revenue than others Bottleneck providers may not have incentive to upgrade Efficiency decreases quickly as network size gets larger

24. 24 Without bottleneck: Outcome of the Nash Game (cont) Bottleneck provider always charges more … p1p1 p2p2 p 2 * (p 1 ) p 1 * (p 2 ) constraint due to Provider 2 p 2 * (p 1 ) under constraint Assume C 1 > C 2 The smaller C 2 is, the larger the ratio p 2 * /p 1 * is.

25. 25 Outcome of the Nash Game (cont) Bottleneck providers may lack incentive to upgrade Again assume C 1 > C 2. It can be shown that when provider 2’s constraint is active, so that may have a solution, i.e. a maximizer may exist, so that J 2 may not always increase with C 2.

26. 26 Outcome of the Nash Game (cont) Example: demand d(p) = Aexp( − Bp  ),  >1 J2*J2* J1*J1* capacity unconstrained

27. 27 Improve Outcome of the Game Approach A: centralized allocation –Prices are chosen to maximize the total revenue –Main challenge: ▪ Individual provider’s benefit vs. social welfare Approach B: cooperative games –Pareto-efficient allocation among providers –Fairness defined through set of axioms ▪ Generalized Nash’s bargaining solution

28. 28 Nash’s Bargaining Solution The equilibrium should satisfy payoff J 1 payoff J 2 feasible payoff set A B C J2J2 J1J1 Pareto-efficient set Generalize to n-player case Proportional Fairness Criteria

29. 29 An Example N access backbone C Solution : where Unfair allocation biased against backbone provider

30. 30 Modified Bargaining Solution A two-level bargaining approach –Proportionally-fair split of revenue collected on each route r –Bargaining on per-provider basis for the total price per route FACT: Equal sharing on each route.

31. 31 Modified Bargaining Solution: Example C1C1 d(p) p 31 p1p1 C2C2 p 32 100 ¢ d(p) 10 ¢ d(p) p2p2 p3p3 d1d1 d3d3 d2d2 d3d3 In general, it is difficult to compute the solution in a decentralized way (not scalable).

32. 32 Our Approach Trade Pareto-efficiency with scalability –Providers still share revenue on a per-route basis –but compute equilibrium total price p r through Nash game Advantages –No need of knowing individual capacity constraints –Can be implemented by a distributed protocol (scalable) –Can eliminate drawbacks of non-cooperative pricing

33. 33 Example Revisited C1C1 d 2 (p) p 31 p1p1 C2C2 p 32 d 1 (p) d 3 (p ) p2p2 p3p3 Provider 1 Provider 2 Best-response:

34. 34 Optimality Condition For a route r on link i (general network topology) marginal cost on link i “locally optimal” total price for the route sum of prices charged by other providers hop count A system of N such equations for each flow

35. 35 Optimal Price: solution  feasible set of , there is a unique solution to the price that links should mark for flows on a route r if link i has the largest  i, on all other links, ) Only the most “congested” link on a route marks price Each provider solves its  i based on local constraints –A Nash game with  i as strategy –Pure-strategy Nash equilibrium exists in this game (proof by Brower’s fixed-point theorem)

36. 36 Properties of the Equilibrium Compare with centralized approach Centralized : Sharing : Incentive to upgrade –Upgrade will always increase bottleneck providers’ revenue Efficient when capacities are adequate –It is the same as that in centralized allocation –Revenue per provider strictly dominates that in Nash game

37. 37 Distributed Implementation flows on route r 1 i N N r = 0  r s = 0 … … N r =N r + 1  r s = max (  r s,  i ) Can be shown to converge to the Nash equilibrium, by using Lyapunov function

38. 38 A Numerical 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 s 1 = s 2 = s 3 =1

39. 39 What about cost? Net-benefit of a provider = revenue – unit cost £ load –Weighted proportionally-fair allocation on each route ) Equal return on investment New objective function New optimal price How to solicit true cost info from the providers? How to solicit true cost info from the providers?

40. 40 Summary and Future Work Summary –Non-cooperative pricing between providers may be unfair, inefficient and discourage the evolution of the Internet –Cooperative pricing help increase providers’ revenue and lead to more efficient use of the network resources Future work (ongoing) –Bounds on the loss of efficiency due to Nash implementation –Adding competition (routing) to the models –Efficient architecture for revenue distribution

41. Wi-Fi Pricing How can they conduct their transaction? –Pre-pay?  Access Point might take the money and run. –Post-pay?  Client might enjoy service and not pay. –Pay as she goes? Will this payment model work? –Will the access point charge a fixed price over session duration? –Will client and access point accept this payment model at all? Client Access Point

42. 42 General Formulation ptpt Access Point Discrete time slot model : 12 t... Access point proposes price at the start of a slot : Accept Quit Game Client’s Choices :

43. 43 Web Browsing Model of Client Utility Client’s session utility : Note: Asymmetric information: –Access Point knows the distribution of (U,  ) –Client knows the sample value of (U,  ) U : utility per slot T : # slots client ends up buying  : # slots client interested in buying

44. 44 File Transfer Model of Client Utility Client’s utility a step function. Utility #slots connected Asymmetric information: –Access Point knows distribution of  –Client knows the sample value of   

45. 45 Summary of Results Web Browsing Model –Access point charges a constant price. –Clients with high enough utilities connect. File Transfer Model: –Clients are “pessimistic” and refuse to pay anything until the last time slot. –Access Point price not constant.