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Exploring Business Models and Dynamic Formulation Offline Pricing - - PowerPoint PPT Presentation

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Introduction Problem Exploring Business Models and Dynamic Formulation Offline Pricing Frameworks for SPOC Services Combinatorial Auction VCG Mechanism VVCA Mechanism Zhengyang Song, Yongzheng Jia, and Wei Xu Online Combinatorial

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Exploring Business Models and Dynamic Pricing Frameworks for SPOC Services

Zhengyang Song, Yongzheng Jia, and Wei Xu

Tsinghua University

August 24, 2018

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Outline

1 Introduction 2 Problem Formulation 3 Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

4 Online Combinatorial Auction

iBundle

5 Conclusion

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

MOOC platforms

Coursera: 3133 courses EdX: 2293 courses XuetangX: 1507 courses

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

How do they generate revenue?

B2C (Business-to-Customer) Verified Certificates Specializations Online Micro Masters Advanced Placement B2B (Business-to-Business) sub-licensing MOOC contents

  • n-campus SPOC platforms
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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

SPOC services

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Why do we need an auction?

A Bundle of User’s Demand MOOC contents Teaching assistant services SaaS services Technical supports However, resources are limited.

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Notations

[X]: set {1, 2, . . . , X} C: number of available courses N: number of users K: number of steps for negotiation Bn,k: the bundle of user n for step k vn,k: the valuation of user n for his k-th bundle sn,k,c: number of enrollments for course c in bundle Bn,k wn,k,c: operational cost for course c in bundle Bn,k qc: enrollment capacity of course c xn,k ∈ {0, 1}: whether bidder n wins his k-th bundle pn,k: the price we charge for bidder n’s k-th bundle.

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

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Conclusion References

Auction Mechanism Design

Allocation Rule xn,k = A(Bn,k, vn,k, R) =    1 Accept Reject ∀k ∈ [K], n ∈ [N] Pricing Rule pn,k = P(Bn,k, vn,k, R)

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Problem Formulation

maximize:

  • n∈[N],k∈[K]

(pn,k − dn,k −

  • c∈[C]

ωn,k,c) · xn,k (1) s.t.

  • k∈[K]

xn,k ≤ 1, ∀n ∈ [N]; (2a)

  • k∈[K]
  • n∈[N]

sn,k,c · xn,k ≤ qc, ∀c ∈ [C]; (2b) xn,k ∈ {0, 1}, ∀n ∈ [N], ∀k ∈ [K]. (2c)

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

VCG Mechanism [PR03]

Allocation Rule: max

  • n∈[N]
  • k∈[K]

vn,kxn,k s.t. Constraints (2a) - (2c) Payment Rule: pi =

  • j=i
  • k∈[K]

vj,k ˜ xj,k −

  • j=i
  • k∈[K]

vj,kxj,k where ˜ xj,k = arg max

xj,k

  • j=i
  • k∈[K]

vj,kxj,k

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Example - VCG

Bidding vA,{P} = 5, vB,{Q} = 1, vC,{P,Q} = 16

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Example - VCG

Formulation max 5 · xA,{P} + xB,{Q} + 16 · xC,{P,Q} (3) s.t. xA,{P} + xC,{P,Q} ≤ 1 (4a) xB,{Q} + xC,{P,Q} ≤ 1 (4b) xA,{P}, xB,{Q}, xC,{P,Q} ∈ {0, 1} (4c) Allocation xA,{P} = xB,{Q} = 0, xC,{P,Q} = 1

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Example - VCG

Formulation without user C max 5 · xA,{P} + xB,{Q} (5) s.t. xA,{P} ≤ 1 (6a) xB,{Q} ≤ 1 (6b) xA,{P}, xB,{Q} ∈ {0, 1} (6c) Allocation without C ˜ xA,{P} = ˜ xB,{Q} = 1

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Example - VCG

Pricing Pc =

  • ˜

xA,{P} · vA,{P} + ˜ xB,{Q} · vB,{Q}

  • −
  • xA,{P} · vA,{P} + xB,{Q} · vB,{Q}
  • =

(1 · 5 + 1 · 1) − (0 · 5 + 0 · 1) = 6

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Virtual Valuation Mechanism [LS04]

Allocation Rule: max

  • n∈[N]
  • k∈[K]

(µnvn,kxn,k + λn,kxn,k) s.t. Constraints (2a) - (2c) where µ are positive, λn,k is for particular bidder n and bundle k. For example, to ensure bidder n never gets bundle k for a price below p0, set λn,k = −p0.

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Virtual Valuation Mechanism

Payment Rule: pi = 1 µi  

j=i

  • k∈[K]

(µjvj,k ˜ xj,k + λj,k ˜ xj,k − µjvj,kxj,k − λj,kxj,k)   − 1 µi

  • k∈[K]

λi,kxi,k where ˜ xj,k = arg max

xj,k

 

j=i

  • k∈[K]

µjvj,kxj,k + λj,kxj,k  

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Example - VVCA

Bidding vA,{P} = 5, vB,{Q} = 1, vC,{P,Q} = 16

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Example - VVCA

Formulation We assign the following λ, µ: µC = 0.5, λB,{Q} = 1 Now the integer programming would become: max 5 · xA,{P} + xB,{Q} + xB,{Q} + 0.5 · 16 · xC,{P,Q} s.t. Constraints (4a) - (4c) Allocation xA,{P} = xB,{Q} = 0, xC,{P,Q} = 1

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Example - VVCA

Formulation Without C Without the presence of C, we have: max 5 · xA,{P} + xB,{Q} + xB,{Q} s.t. Constraints (6a) - (6c) Allocation without C ˜ xA,{P} = ˜ xB,{Q} = 1

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Example - VVCA

Pricing p′

C

= 1 µC

  • ˜

xA,{P} · vA,{P} + ˜ xB,{Q} · vB,{Q} + λB,{Q}˜ xB,{Q} · vB,{ − 1 µC

  • xA,{P} · vA,{P} + xB,{Q} · vB,{Q}λB,{Q}xB,{Q} · vB,{Q}

= 1 0.5(1 · 5 + 1 · 1 + 1 · 1 · 1) − 1 0.5(0 · 5 + 0 · 1 + 1 · 0 · 1) = 14 Thus the revenue of VVCA mechanism would be 14, which is much higher than the revenue of VCG mechanism, i.e., 6.

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

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Conclusion References

Business Process in MOOC Industry

Algorithm 1: Negotiation between user n and the platform

1 Initialization: Set t = 1 and flag = 0. Suppose the current

status of resource capacity is R.

2 while t ≤ T do 3

(a) User n submits his bids (Bn,k, vn,k) to the platform.

4

(b) The platform calculates xn,k and pn,k, and sends the response message to the user.

5

(c) If accepted, then the negotiation succeeds, update R, set flag = 1, and break. Else (i.e. rejected) the negotiation continues with t = t + 1.

6 end 7 If flag = 0, then the negotiation fails.

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

iBundle [PU00]

maintain ask prices and provisional allocation bid is competitive if it is not lower than ask price bidder is competitive if he has at least one competitive bids Algorithm for each round, bidders submit bids on bundles provisional allocation computed to maximize seller’s revenue terminate if each competitive bidder receives a bundle in the provisional allocation

  • .w., ask prices are increased by a preset parameter,

feedbacks are provided to bidders

  • n termination, provisional allocation becomes the final

allocation, the bidders pay their final bid prices.

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

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Conclusion References

Conclusion

What we have done Model formulation for SPOC services Mechanisms for Offline combinatorial auction Mechanisms for Online combinatorial auction Future Work Compare different mechanisms by simulation Real Data Analysis of SPOC Services

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

iBundle

Conclusion References

Reference

[LS04] Anton Likhodedov and Tuomas Sandholm. Methods for boosting revenue in combinatorial auctions. In AAAI, pages 232–237, 2004. [PR03] Aleksandar Pekeˇ c and Michael H Rothkopf. Combinatorial auction design. Management Science, 49(11):1485–1503, 2003. [PU00] David C Parkes and Lyle H Ungar. Iterative combinatorial auctions: Theory and practice. AAAI/IAAI, 7481, 2000.

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Introduction Problem Formulation Offline Combinatorial Auction

VCG Mechanism VVCA Mechanism

Online Combinatorial Auction

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Conclusion References

Thanks!