Issues in Pricing Internet Services

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

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. 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. 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. Pricing Differentiated Services: Base Model Users choose the service class which maximizes their net benefit p1 strategic users p2 • Delay Ti: 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 If users do not randomize their choices, what kind of equilibrium would happen?

6. Outcome A. Prisoner’s Dilemma H. P. f(T1) = 14 f(T2) = 5 f(T0) = 9 p1= 4 p2= 1 A p1 B p2 L. P. B H. P. L. P. A 9-4 = 5 9-4 = 5 14-4 =10 5-1 = 4 NE H. P. 9-1 = 8 9-1 = 8 5-1 = 4 14-4 =10 L. P.

7. Outcome B. No Pure-Strategy Equilibrium T1 T0 T2 p1= 4 p2= 1 A p1 13 9 7 f1 f2 B 11 9 5 p2 B H. P. L. P. A 9-4 = 5 9-4 = 5 13-4 = 9 5-1 = 4 H. P. 9-1 = 8 9-1 = 8 7-1 = 6 11-4 = 7 L. P.

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

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

10. stable but inefficient equilibrium  Properties of Equilibrium: an example • Utility function f is concave; strict-priority scheduling unstable equilibrium p1-p2 1 1! x1!search2which satisfies

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

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

13. where k is a bound on 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 pi,pi(xi) • Choose pi(xi) so that M<0 under perturbation • Resulting equilibrium is stable, if No congestion externality between classes ) always stable p1 users p2

14. bid:  agent (VCG) D1 user D2 charge:pi To be more efficient… • 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 Effect on last user in L.P. Effect on last user in H.P. and L.P.

15. pi Di Our Solution • Congestion pricing • Equilibrium p1 user p2 two marginal users equilibrium prices externality cost of the marginal users Users choose to join H.P. to L.P. in decreasing order of 

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

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. A Possible Implementation ACK $3 request $1 $2 request Provider 1 Provider2 request $1 How should each provider price its share of service?

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. 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 • Revenuepd(p) has a unique maximizer • For use later, define

21. provider 1 Model - Providers • Local capacity limit is private information • QoS requirements and routes are fixed and are independent from prices charge p1+p2 + p1 + p2 provider 2 demand p1+p2 • Revenue = Price £ Demand • Choose price to maximize its own revenue, while regulate the load to meet QoS requirement

22. Formulation: an example p1 p2 demand = d(p1+p2) 1 2 D • • • C2 C1 Provider 1 Provider 2 • A pricing game between two providers • Different solution concepts may apply, depend on actual implementation • Nash game mostly suited for large networks

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. constraint due to Provider 2 p2*(p1) under constraint Outcome of the Nash Game (cont) • Bottleneck provider always charges more … p2 Assume C1> C2 Without bottleneck: p1*(p2) The smaller C2is, the larger the ratio p2*/p1*is. p2*(p1) p1

25. Outcome of the Nash Game (cont) • Bottleneck providers may lack incentive to upgrade Again assume C1 > C2. 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 J2 may not always increase with C2.

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

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

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

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. Modified Bargaining Solution: Example d3 d3 p31 p32 p3 10¢d(p) d(p) 100¢d(p) p1 p2 C1 C2 d1 d2 In general, it is difficult to compute the solution in a decentralized way (not scalable).

32. Our Approach • Trade Pareto-efficiency with scalability • Providers still share revenue on a per-route basis • but compute equilibrium total price pr 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. Example Revisited p31 p32 p3 d3(p) d2(p) p1 p2 d1(p) C1 C2 Provider 1 Provider 2 Best-response:

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

35. Optimal Price: solution •  feasible set of m, there is a unique solution to the price that links should mark for flows on a route r if link i has the largest mi, 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 ias strategy • Pure-strategy Nash equilibrium exists in this game (proof by Brower’s fixed-point theorem)

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

38. A Numerical Example r2 r4 s1 = s2= s3 =1 r1 r3 C2=5 C1=2 C3=3 demand = 10 exp(-p2) on all routes prices i p2 link 1 p3 p1 link 3 p4 link 2

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 How to solicit true cost info from the providers? New optimal price

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. Access Point Client 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?

42. ... t 1 2 Access Point General Formulation Discrete time slot model: Access point proposes price at the start of a slot: pt Accept Client’s Choices: Quit Game

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. 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. 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.