1. Pricing for Revenue Maximization in IoT Data Markets: An Information Design Perspective
Weichao Mao, Zhenzhe Zheng, Fan Wu
Shanghai Jiao Tong University, China
May 2, 2019

2. Outline Motivation Preliminaries Pricing Mechanisms Evaluation Results
Simple Setting: Single Buyer Type
General Setting: Multiple Buyer Types
Practical Considerations
Evaluation Results
Summary

3. Outline Motivation Preliminaries Pricing Mechanisms Evaluation Results
Simple Setting: Single Buyer Type
General Setting: Multiple Buyer Types
Practical Considerations
Evaluation Results
Summary

4. Data Markets For targeted advertising: For city services:
Gnip, Inc.: support.gnip.com
HERE Technologies:
IOTA:
DataBroker DAO: databrokerdao.com

5. Challenges: Time Sensitiveness
Historical data vs. Future data

6. Challenges: Data Piracy
Raw data vs. Data services
Raw Data
Raw Data

7. Challenges: Data Valuation
Data Valuation independent of Data Volume

8. Design Objective
Propose a market model to capture the unique economic properties of IoT data.
Present pricing mechanisms that maximize seller revenue in the corresponding market model.

9. Outline Motivation Preliminaries Pricing Mechanisms Evaluation Results
Simple Setting: Single Buyer Type
General Setting: Multiple Buyer Types
Practical Considerations
Evaluation Results
Summary

10. State & Action Nature state set Ω={ 𝜔 1 = , 𝜔 2 = } Action set
Ω={ 𝜔 1 = , 𝜔 2 = }
Action set
𝐴={ 𝑎 1 = , 𝑎 2 = }

11. Utility Matrix Buyer utility matrix: action 𝑎
𝑢 𝜔 1 , 𝑎 1 =𝟏 𝑢 𝜔 1 , 𝑎 2 =0 𝑢 𝜔 2 , 𝑎 1 = 𝑢 𝜔 2 , 𝑎 2 =𝟏
state 𝜔
action 𝑎

12. Type & Prior Utility
Buyer prior estimation, or type 𝜽= 𝜃 1 =0.7, 𝜃 2 =0.3
𝑃𝑟𝑜𝑏 𝜔= =0.7,
𝑃𝑟𝑜𝑏 𝜔= =0.3
Buyer prior utility 𝑢 1 = max 𝑎 𝐸 𝜔 𝑢 𝜔,𝑎 .
𝑢 =Prob ×𝑢 Prob ×𝑢( )
=0.7×1+0.3×0= 𝟎.𝟕

13. Menu Seller publishes a menu of pricing schemes 𝑀= 𝐼, 𝑡 𝐼
Experiment 𝐼 and the corresponding price 𝑡 𝐼
In experiment ②, if 𝜔= 𝜔 1 : Send signal 𝑠 1 ( ) with 𝑝 𝑠 1 𝜔 1 =0.8, and send 𝑠 2 ( ) with 𝑝 𝑠 2 𝜔 1 =0.2

14. Bayesian Updating
Buyer updates his belief and gets posterior estimation:
𝑝 𝜔 𝑖 𝑠 𝑗 = 𝑝 𝑠 𝑗 𝜔 𝑖 ⋅𝑝( 𝜔 𝑖 ) 𝑝( 𝑠 𝑗 )
Prob 𝜔= | 𝒔 𝟏 =0.86,
Prob 𝜔= | 𝒔 𝟏 =0.14
Suppose buyer receives in experiment ②:

15. Buyer Valuation Buyer expected posterior utility:
𝑢 2 = 𝑗 𝑝( 𝑠 𝑗 ) max 𝑎 𝑖=1 𝑛 𝑝 𝜔 𝑖 𝑠 𝑗 ⋅𝑢( 𝜔 𝑖 ,𝑎) =𝟎.𝟕𝟕
Utility increment, or buyer valuation:
𝑣 𝜽, 𝐼 2 = 𝑢 − 𝑢 =𝟎.𝟎𝟕
Set price 𝑡 𝐼 =𝟎.𝟎𝟓, and get revenue 0.05
Individual rationality (I.R.): 𝑣=𝑢 2 − 𝑢 1 =0.07>0.05= 𝑡 𝐼

16. Two Important Experiments
Full-information experiment:
𝐼 =
100% accurate data, leading to highest utility increment
No-information experiment:
𝐼 =
Random data, leading to zero utility increment
Alternative: let 𝑆 be a singleton
In our example: 𝑣 𝜽, 𝐼 =0.3, leads to highest revenue.

17. Data Trading Process

18. Outline Motivation Preliminaries Pricing Mechanisms Evaluation Results
Simple Setting: Single Buyer Type
General Setting: Multiple Buyer Types
Practical Considerations
Evaluation Results
Summary

19. The MSimple Mechanism
Only one buyer type 𝜽 exists, and 𝜽 is known to the seller
Theorem 1: For the single buyer type case, the optimal menu contains one pricing scheme, which is a full-information experiment with a price equal to the buyer’s valuation.

20. Outline Motivation Preliminaries Pricing Mechanisms Evaluation Results
Simple Setting: Single Buyer Type
General Setting: Multiple Buyer Types
Practical Considerations
Evaluation Results
Summary

21. General Setting: Multiple Buyer Types
Buyers have different prior estimations, and the seller cannot tell buyers apart.
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟕,
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟑
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟒,
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟔
Distribution of buyer types 𝐹 𝜽 ∈ΔΘ is public information.

22. Second Degree Price Discrimination
A separate pricing scheme 𝐼 𝜃 , 𝑡 𝜃 for each type 𝜃∈Θ.
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟕,
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟑
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟒,
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟔
Incentive compatible (I.C.):
𝑣 𝜽, 𝐼 𝜽 − 𝑡 𝜽 ≥𝑣 𝜽, 𝐼 𝜽 ′ − 𝑡 𝜽 ′ , ∀𝜽, 𝜽 ′ .

23. The MGeneral Mechanism
Theorem 2: For multiple buyer types, the revenue maximizing menu can be solved in polynomial time of |Ω| and Θ , by solving a convex program.

24. Back to the Example The revenue-maximizing menu:
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟕,
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟑
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟒,
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟔
Extracting full surplus from , but not from
The optimal revenue is 0.6

25. Practical Considerations
The weaknesses of MGeneral?
Price discrimination is unfair.
Heavy computation.
Menu size as big as |Θ|.

26. Outline Motivation Preliminaries Pricing Mechanisms Evaluation Results
Simple Setting: Single Buyer Type
General Setting: Multiple Buyer Types
Practical Considerations
Evaluation Results
Summary

27. The MPractical Mechanism
Consider a constant-size menu:
where 𝑡 is the optimal fixed price:

28. Performance of MPractical
Theorem 3: MPractical extracts at least a logarithmic fraction Ω( 1 log|Θ| ) of the full surplus even in the worst case.
Theorem 4: No constant-size menu can extract more than a logarithmic fraction 𝑂( 1 log|Θ| ) of the full surplus in the worst case.

29. Back to the Example The optimal menu:
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟕,
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟑
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟒,
𝑃𝑟𝑜𝑏 𝜔= =𝟎.𝟔
Extracting full surplus from , but not from
The optimal revenue is 0.6

30. Outline Motivation Preliminaries Pricing Mechanisms Evaluation Results
Simple Setting: Single Buyer Type
General Setting: Multiple Buyer Types
Practical Considerations
Evaluation Results
Summary

31. Evaluation Results
Varying |Θ|:

32. Outline Motivation Preliminaries Pricing Mechanisms Evaluation Results
Simple Setting: Single Buyer Type
General Setting: Multiple Buyer Types
Practical Considerations
Evaluation Results
Summary

33. Summary
We characterize the unique economic properties of IoT data, and propose a market model from an information design perspective to capture these properties.
We extract full surplus in the simple setting, and formulate the revenue maximization problem in the general setting as a polynomial convex program.
We consider a more practical setting, and propose a constant size mechanism that achieves tight logarithmic approximation ratio.

34. Thank you!