1 / 45

Issues in Pricing Internet Services

Issues in Pricing Internet Services. Linhai He & Jean Walrand Dept of EECS, U.C. Berkeley March 8, 2004. Challenges. Stagnant telecommunication industry “We know how to route packets; what we don’t know how to do is route dollars.” - David Clark, MIT.

cyndi
Télécharger la présentation

Issues in Pricing Internet Services

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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.

More Related