Revenue Management for Communication Networks

1. Revenue Management for Communication Networks Information Engineering Department The Chinese University of Hong Kong Jianwei Huang Joint work with Helen Li and Bob Li

2. Introduction: Network Economics Network details: • Revenue management: • to sell the right resources to the right customers at the right time and the right price. Heterogeneity of users, technologies, applications… Service Provide Revenue management: how to set the prices to maximize the revenue?

3. Outline • Introduction • Model • Revenue maximization under Complete Information • Complete Price Differentiation • Single Price Scheme (No Differentiation) • Partial Price Differentiation • Revenue maximization under Incomplete Information • Differentiation Schemes • Conclusion

4. A Service provider Admitted to access Network Model • One SP • S: Total limited resource • Igroups of users • Indexed by i=1,2,…I • For group i: • Ni homogeneous users • ni : admitted users • ui(si)=θi log(1+si) : Utility function • si: allocated resource • θi:willingness to pay • pi: Price per unit resource of group i • Assume θ1 >θ2 >…>θI S: total resource (N1, n1, u1, s1, p1 ) (N3, n3, u3, s3, p3 ) (N2, n2, u2, s2, p2 ) N2 = 3 n2 = 2 Utility: u2(s2) =θ2 log(1+ s2) Surplus: u2(s2) – p2s2

5. No, Design a price menu SP must guarantee determine (pi,ni) Two-stage System Model • Complete price differentiation • Single price scheme • Partial price differentiation Stage 1: SP sets the price Complete information? complexity revenue Yes Stage 2: an admitted user Chooses the quantity si Possible to realize differentiation schemes Two-stage System model (Stackelberg Game) Consider the incentives of both SP and users

6. Outline • Introduction • Model • Revenue maximization under Complete Information • Complete Price Differentiation • Single Price Scheme (No Differentiation) • Partial Price Differentiation • Revenue maximization under Incomplete Information • Differentiation Schemes • Conclusion

7. (pi,ni) Complete Information: Stage 2 • A group i user admitted in stage 1 • given price pi • maximize his surplus by choosing the proper resource quantity: Stage 1: SP sets the price Complete information? Yes Stage 2: an admitted user Chooses the quantity si

8. (pi,ni) Complete Price Differentiation Stage 1: SP sets the price Complete information? Yes Difficulties: • Non-convex objective • Integer variables • Coupled constraint Method: decomposition • Resource allocation subproblem • Admission control subproblem Stage 2: an admitted user Chooses the quantity si SP’s pricing and admission control problem:

9. Complete Price Differentiation (con’t) Solution Intuition • Prices can perform admission control • Threshold structure • All users are admitted • There exist a group threshold Kcp and λ*, such that Indicates to allocate resource to high willingness to pay users with priority Total resource S Prices are too high to deman any resource Effective market Kcp=4 1 2 3 4 5 6 Group i θ1 >θ2 >…>θI group1 group2 group3 group4 group5 group6 Kcp=4 Nonzero resource Zero resource

10. Outline • Introduction • Model • Revenue maximization under Complete Information • Complete Price Differentiation • Single Price Scheme (No Differentiation) • Partial Price Differentiation • Revenue maximization under Incomplete Information • Differentiation Schemes • Conclusion

11. Single Price Scheme (No differentiation) SP charge a single price to all groups Solution • All users are admitted • There exist a group threshold Ksp and p*, such that Remark: Similar threshold structure as the complete price differention

12. Special Properties of Single Price Scheme Effective market Super-group group1 group2 group3 group4 group5 group6 Ksp=4 Nonzero resource Zero resource A smaller effective market : The effective market can be equivalent to a “Super-group” where Under single price scheme:

13. When is price differentiation most beneficial? complexity revenue Peak points indicate the chages of effective market under the single price shceme • High differentiation gain: • High willingness to pay users are minorities • Resource are comparativelly limited • A three-group example • But what if the number of user type is large…

14. Outline • Introduction • Model • Revenue maximization under Complete Information • Complete Price Differentiation • Single Price Scheme (No Differentiation) • Partial Price Differentiation • Revenue maximization under Incomplete Information • Differentiation Schemes • Conclusion

15. Partial Price Differentiation Ex: Charge 6 groups with 2 prices Partition I groups into J clusters: S(I, J) group1 group2 group3 group4 group5 group6 p1 =p1=p2=p3 p2 =p4=p5=p6 • General formulation: • Including CP (J=I) and SP (J=1) as special cases • Difficulties: • Combinatorial optimization problem SP charges J (J ≤ I)prices to I groups

16. Solving Parital Price Differentiation group1 group1 group2 group3 group4 group3 group5 group4 group5 group2 group6 group6 0 0 Kpp=4 • First: reduce search space • Optimal partitions involve consecutive group indices within clusters • Intuition: high willingness to pay groups have priority • Transfer into three (nested) sub-problems • Optimal partition into clusters • In each cluster: single pricing problem • Among clusters: complete price differentiation problem • Polynomial time (O(IJ) ) algorithm

17. Trade-off: Complexity Vs. Revenue Note: High willingness to pay users are minorities When S=100 Partition price differentiation : a five-group example

18. Outline • Introduction • Model • Revenue maximization under Complete Information • Complete Price Differentiation • Single Price Scheme (No Differentiation) • Partial Price Differentiation • Revenue maximization under Incomplete Information • Differentiation Schemes • Conclusion

19. No, statistical information only SP must guarantee (pi,ni) CP under Incomplete Information Stage 1: SP sets the price Complete information? Yes The higher the quantity, the higher the price. I: the total number of groups Nis: the number of users in each group uis: the utility function of each group Stage 2: an admitted user Chooses the quantity si But The SP doesn’t know which group each user belongs to. • Incomplete Information • Challenge: Possible to realize price differentiation? • Method: Make the users self-differentiation • SP: publishes the quantity-based price menu. • Users: freely choose their quantities.

20. CP under Incomplete Information (con’t) Aim: to properly set the thresholds to make the users self-differentiated to get the same result just as the complete price differentiation scheme. CP:θ1> θ2, s1*>s2*, p1*>p2* Low pricep2* High pricep1* Consider two-group case: • group 1 chooses higher price p1*at quantity s1* • group 2 chooses lower price p2 *at quantity s2* θ1 log(1+s1)-p2*s1 √ θ1 log(1+s1)-p1*s1

21. CP under Incomplete Information • Complete Price differentiation can be reached when the following condition is satisfied: for q=1,…Kcp-1 • Similar result may be extended to partial price differentiation

22. Outline • Introduction • Model • Revenue maximization under Complete Information • Complete Price Differentiation • Single Price Scheme (No Differentiation) • Partial Price Differentiation • Revenue maximization under Incomplete Information • Differentiation Schemes • Conclusion

23. No, statistical information only (pi,ni) Conclusion • Complete price differentiation • Single price scheme • Partial price differentiation Stage 1: SP sets the price Complete information? complexity Efficient Algorithms Yes revenue SP must guarantee Stage 2: an admitted user Chooses the quantity si Sufficient condition for realizing price differentiation Possible to realize differentiation schemes

24. Contact Jianwei Huang Network Communications and Economics Lab http://ncel.ie.cuhk.edu.hk/

25. When is price differentiation most benifical? where Ratio of willingness to pays total number of the users the percentage of group 1 users (high willingness to pay users) the level of normalized available resource • Differentiation Gain • Consider a simple two-group case:

26. Differentiation Gain in a Two-group Cases • Fix αandk, for parameter t • (1) Ksp=2, Kcp=2 • (2) Ksp=1, Kcp=2 • (3) Ksp=1, Kcp=1 (CD degenerates to SP) • Define • Differentiation gain is large when: • α is small → high willingness to pay users are minorities • k is small → resource is limited

27. CP under Incomplete Information • Complete Price differentiation can be reached when the following condition is satisfied: for q=1,…Kcp-1 where tqis the unique solution of over the domain t >1. • Corollary: • tqis upper bounded bytq<troot≈ 2.21846, for q=1,…K-1, • trootis the root of the equation • Similar result can be extended to partial price differentiation