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

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

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

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

Challenges: Time Sensitiveness Historical data vs. Future data

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

Challenges: Data Valuation Data Valuation independent of Data Volume

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.

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

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

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

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 1 =Prob ×𝑢 +Prob ×𝑢( ) =0.7×1+0.3×0= 𝟎.𝟕

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

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:

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 2 − 𝑢 1 =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

Two Important Experiments Full-information experiment: 𝐼 = 1 0 0 1 100% accurate data, leading to highest utility increment No-information experiment: 𝐼 = 0.5 0.5 0.5 0.5 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.

Data Trading Process

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

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.

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

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.

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 ′ .

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.

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

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

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

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

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.

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

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

Evaluation Results Varying |Θ|:

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

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.

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