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

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 Auction iBundle Tsinghua University Conclusion References August 24, 2018

Outline 1 Introduction Introduction Problem Formulation 2 Problem Formulation Offline Combinatorial Auction 3 Offline Combinatorial Auction VCG Mechanism VCG Mechanism VVCA Mechanism VVCA Mechanism Online Combinatorial Auction iBundle 4 Online Combinatorial Auction Conclusion iBundle References 5 Conclusion

MOOC platforms Introduction Problem Formulation Offline Combinatorial Coursera: 3133 courses Auction VCG Mechanism EdX: 2293 courses VVCA Mechanism XuetangX: 1507 courses Online Combinatorial Auction iBundle Conclusion References

How do they generate revenue? B2C (Business-to-Customer) Introduction Problem Verified Certificates Formulation Offline Specializations Combinatorial Auction Online Micro Masters VCG Mechanism VVCA Mechanism Advanced Placement Online Combinatorial Auction B2B (Business-to-Business) iBundle Conclusion References sub-licensing MOOC contents on-campus SPOC platforms

SPOC services Introduction Problem Formulation Offline Combinatorial Auction VCG Mechanism VVCA Mechanism Online Combinatorial Auction iBundle Conclusion References

Why do we need an auction? Introduction Problem A Bundle of User’s Demand Formulation Offline MOOC contents Combinatorial Auction Teaching assistant services VCG Mechanism VVCA Mechanism SaaS services Online Combinatorial Technical supports Auction iBundle Conclusion However, resources are limited. References

Notations [ X ]: set { 1 , 2 , . . . , X } Introduction C : number of available courses Problem Formulation N : number of users Offline K : number of steps for negotiation Combinatorial Auction B n , k : the bundle of user n for step k VCG Mechanism VVCA Mechanism v n , k : the valuation of user n for his k -th bundle Online Combinatorial s n , k , c : number of enrollments for course c in bundle B n , k Auction iBundle w n , k , c : operational cost for course c in bundle B n , k Conclusion q c : enrollment capacity of course c References x n , k ∈ { 0 , 1 } : whether bidder n wins his k -th bundle p n , k : the price we charge for bidder n ’s k -th bundle.

Auction Mechanism Design Allocation Rule Introduction Problem Formulation  Offline 1 Accept Combinatorial  Auction x n , k = A ( B n , k , v n , k , R ) = ∀ k ∈ [ K ] , n ∈ [ N ] VCG Mechanism 0 Reject VVCA  Mechanism Online Combinatorial Auction iBundle Pricing Rule Conclusion References p n , k = P ( B n , k , v n , k , R )

Problem Formulation Introduction Problem � � maximize: ( p n , k − d n , k − ω n , k , c ) · x n , k (1) Formulation Offline n ∈ [ N ] , k ∈ [ K ] c ∈ [ C ] Combinatorial Auction s.t. VCG Mechanism VVCA � Mechanism x n , k ≤ 1 , ∀ n ∈ [ N ]; (2a) Online k ∈ [ K ] Combinatorial Auction � � iBundle s n , k , c · x n , k ≤ q c , ∀ c ∈ [ C ]; (2b) Conclusion k ∈ [ K ] n ∈ [ N ] References x n , k ∈ { 0 , 1 } , ∀ n ∈ [ N ] , ∀ k ∈ [ K ] . (2c)

VCG Mechanism [PR03] Allocation Rule: Introduction � � max v n , k x n , k Problem Formulation n ∈ [ N ] k ∈ [ K ] Offline Combinatorial s.t. Constraints (2a) - (2c) Auction VCG Mechanism VVCA Payment Rule: Mechanism Online Combinatorial Auction iBundle � � � � p i = v j , k ˜ x j , k − v j , k x j , k Conclusion j � = i j � = i k ∈ [ K ] k ∈ [ K ] References where � � x j , k = arg max ˜ v j , k x j , k x j , k j � = i k ∈ [ K ]

Example - VCG Introduction Problem Formulation Offline Bidding Combinatorial Auction VCG Mechanism VVCA Mechanism v A , { P } = 5 , v B , { Q } = 1 , v C , { P , Q } = 16 Online Combinatorial Auction iBundle Conclusion References

Example - VCG Formulation Introduction max 5 · x A , { P } + x B , { Q } + 16 · x C , { P , Q } (3) Problem Formulation s.t. Offline Combinatorial x A , { P } + x C , { P , Q } ≤ 1 (4a) Auction VCG Mechanism VVCA x B , { Q } + x C , { P , Q } ≤ 1 (4b) Mechanism Online x A , { P } , x B , { Q } , x C , { P , Q } ∈ { 0 , 1 } (4c) Combinatorial Auction iBundle Conclusion Allocation References x A , { P } = x B , { Q } = 0 , x C , { P , Q } = 1

Example - VCG Formulation without user C Introduction max 5 · x A , { P } + x B , { Q } (5) Problem Formulation Offline s.t. Combinatorial x A , { P } ≤ 1 (6a) Auction VCG Mechanism VVCA x B , { Q } ≤ 1 (6b) Mechanism Online Combinatorial x A , { P } , x B , { Q } ∈ { 0 , 1 } (6c) Auction iBundle Conclusion Allocation without C References x A , { P } = ˜ ˜ x B , { Q } = 1

Example - VCG Introduction Problem Pricing Formulation Offline Combinatorial Auction � � VCG Mechanism P c = x A , { P } · v A , { P } + ˜ ˜ x B , { Q } · v B , { Q } VVCA Mechanism � � − x A , { P } · v A , { P } + x B , { Q } · v B , { Q } Online Combinatorial = (1 · 5 + 1 · 1) − (0 · 5 + 0 · 1) Auction iBundle = 6 Conclusion References

Virtual Valuation Mechanism [LS04] Allocation Rule: Introduction Problem Formulation Offline � � max ( µ n v n , k x n , k + λ n , k x n , k ) Combinatorial Auction n ∈ [ N ] k ∈ [ K ] VCG Mechanism VVCA Mechanism s.t. Constraints (2a) - (2c) Online Combinatorial Auction where µ are positive, λ n , k is for particular bidder n and bundle iBundle k . Conclusion For example, to ensure bidder n never gets bundle k for a price References below p 0 , set λ n , k = − p 0 .

Virtual Valuation Mechanism Payment Rule: Introduction   Problem 1 Formulation � � p i = ( µ j v j , k ˜ x j , k + λ j , k ˜ x j , k − µ j v j , k x j , k − λ j , k x j , k )  µ i Offline j � = i k ∈ [ K ] Combinatorial Auction 1 VCG Mechanism � − λ i , k x i , k VVCA Mechanism µ i k ∈ [ K ] Online Combinatorial Auction where iBundle Conclusion   References � � ˜ x j , k = arg max µ j v j , k x j , k + λ j , k x j , k  x j , k j � = i k ∈ [ K ]

Example - VVCA Introduction Problem Formulation Offline Bidding Combinatorial Auction VCG Mechanism VVCA Mechanism v A , { P } = 5 , v B , { Q } = 1 , v C , { P , Q } = 16 Online Combinatorial Auction iBundle Conclusion References

Example - VVCA Formulation We assign the following λ, µ : Introduction Problem Formulation µ C = 0 . 5 , λ B , { Q } = 1 Offline Combinatorial Now the integer programming would become: Auction VCG Mechanism VVCA Mechanism max 5 · x A , { P } + x B , { Q } + x B , { Q } + 0 . 5 · 16 · x C , { P , Q } Online Combinatorial s.t. Constraints (4a) - (4c) Auction iBundle Conclusion References Allocation x A , { P } = x B , { Q } = 0 , x C , { P , Q } = 1

Example - VVCA Formulation Without C Introduction Problem Without the presence of C , we have: Formulation Offline Combinatorial max 5 · x A , { P } + x B , { Q } + x B , { Q } Auction VCG Mechanism s.t. Constraints (6a) - (6c) VVCA Mechanism Online Combinatorial Auction Allocation without C iBundle Conclusion References x A , { P } = ˜ ˜ x B , { Q } = 1

Example - VVCA Pricing Introduction Problem Formulation 1 Offline p ′ � = x A , { P } · v A , { P } + ˜ ˜ x B , { Q } · v B , { Q } + λ B , { Q } ˜ x B , { Q } · v B , { Combinatorial C µ C Auction VCG Mechanism 1 VVCA � − x A , { P } · v A , { P } + x B , { Q } · v B , { Q } λ B , { Q } x B , { Q } · v B , { Q } Mechanism µ C Online 0 . 5(1 · 5 + 1 · 1 + 1 · 1 · 1) − 1 1 Combinatorial Auction = 0 . 5(0 · 5 + 0 · 1 + 1 · 0 · 1) iBundle = 14 Conclusion References Thus the revenue of VVCA mechanism would be 14, which is much higher than the revenue of VCG mechanism, i.e., 6.

Business Process in MOOC Industry Algorithm 1: Negotiation between user n and the platform Introduction 1 Initialization: Set t = 1 and flag = 0. Suppose the current Problem Formulation status of resource capacity is R . Offline 2 while t ≤ T do Combinatorial Auction (a) User n submits his bids ( B n , k , v n , k ) to the platform. 3 VCG Mechanism VVCA (b) The platform calculates x n , k and p n , k , and sends the 4 Mechanism response message to the user. Online Combinatorial (c) If accepted , then the negotiation succeeds, update R , Auction 5 iBundle set flag = 1, and break . Else (i.e. rejected ) the Conclusion negotiation continues with t = t + 1. References 6 end 7 If flag = 0, then the negotiation fails.