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On Three-Layer Data Markets

Alireza Fallah, Michael I. Jordan, Ali Makhdoumi, Azarakhsh Malekian

TL;DR

This paper develops a three-layer data market model comprising data owners, platforms, and a data buyer, and analyzes strategic interactions through a multi-stage, subgame-perfect Nash framework. The core method combines a Gaussian-mechanism privacy setup with information-revealing metrics to derive a unique price equilibrium and characterize platform-entry and noise decisions across regimes defined by the buyer’s valuation $\beta$ and platform costs. Key findings show that high buyer valuation induces universal platform entry, zero user utility at equilibrium, and positive buyer utility; low valuation yields entry by only low-cost platforms with zero user utility, while competition nonetheless raises buyer welfare and overall utilitarian welfare grows with platform count. Regulation insights reveal that a ban on data sharing is not universally optimal; uniform minimum privacy mandates can help, and nonuniform mandates (ban low-cost platforms while mandating privacy on high-cost platforms) can further improve user utility under mixed-market conditions, guiding policy design in data markets.

Abstract

We study a three-layer data market comprising users (data owners), platforms, and a data buyer. Each user benefits from platform services in exchange for data, incurring privacy loss when their data, albeit noisily, is shared with the buyer. The user chooses platforms to share data with, while platforms decide on data noise levels and pricing before selling to the buyer. The buyer selects platforms to purchase data from. We model these interactions via a multi-stage game, focusing on the subgame Nash equilibrium. We find that when the buyer places a high value on user data (and platforms can command high prices), all platforms offer services to the user who joins and shares data with every platform. Conversely, when the buyer's valuation of user data is low, only large platforms with low service costs can afford to serve users. In this scenario, users exclusively join and share data with these low-cost platforms. Interestingly, increased competition benefits the buyer, not the user: as the number of platforms increases, the user utility does not necessarily improve while the buyer utility improves. However, increasing the competition improves the overall utilitarian welfare. Building on our analysis, we then study regulations to improve the user utility. We discover that banning data sharing maximizes user utility only when all platforms are low-cost. In mixed markets of high- and low-cost platforms, users prefer a minimum noise mandate over a sharing ban. Imposing this mandate on high-cost platforms and banning data sharing for low-cost ones further enhances user utility.

On Three-Layer Data Markets

TL;DR

This paper develops a three-layer data market model comprising data owners, platforms, and a data buyer, and analyzes strategic interactions through a multi-stage, subgame-perfect Nash framework. The core method combines a Gaussian-mechanism privacy setup with information-revealing metrics to derive a unique price equilibrium and characterize platform-entry and noise decisions across regimes defined by the buyer’s valuation and platform costs. Key findings show that high buyer valuation induces universal platform entry, zero user utility at equilibrium, and positive buyer utility; low valuation yields entry by only low-cost platforms with zero user utility, while competition nonetheless raises buyer welfare and overall utilitarian welfare grows with platform count. Regulation insights reveal that a ban on data sharing is not universally optimal; uniform minimum privacy mandates can help, and nonuniform mandates (ban low-cost platforms while mandating privacy on high-cost platforms) can further improve user utility under mixed-market conditions, guiding policy design in data markets.

Abstract

We study a three-layer data market comprising users (data owners), platforms, and a data buyer. Each user benefits from platform services in exchange for data, incurring privacy loss when their data, albeit noisily, is shared with the buyer. The user chooses platforms to share data with, while platforms decide on data noise levels and pricing before selling to the buyer. The buyer selects platforms to purchase data from. We model these interactions via a multi-stage game, focusing on the subgame Nash equilibrium. We find that when the buyer places a high value on user data (and platforms can command high prices), all platforms offer services to the user who joins and shares data with every platform. Conversely, when the buyer's valuation of user data is low, only large platforms with low service costs can afford to serve users. In this scenario, users exclusively join and share data with these low-cost platforms. Interestingly, increased competition benefits the buyer, not the user: as the number of platforms increases, the user utility does not necessarily improve while the buyer utility improves. However, increasing the competition improves the overall utilitarian welfare. Building on our analysis, we then study regulations to improve the user utility. We discover that banning data sharing maximizes user utility only when all platforms are low-cost. In mixed markets of high- and low-cost platforms, users prefer a minimum noise mandate over a sharing ban. Imposing this mandate on high-cost platforms and banning data sharing for low-cost ones further enhances user utility.
Paper Structure (17 sections, 21 theorems, 153 equations, 4 figures)

This paper contains 17 sections, 21 theorems, 153 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Our model and main results
  3. Related literature
  4. Model
  5. Utility functions
  6. Revealed Information Properties
  7. Preliminary Equilibrium Characterization
  8. Equilibrium Characterization with $K=2$ Platforms
  9. Insights from the case with $K=2$
  10. Equilibrium Characterization with $K>2$ Platforms
  11. Regulation
  12. Conclusion
  13. Acknowledgment
  14. Missing Proofs
  15. Extensions and Additional Results
  16. ...and 2 more sections

Key Result

Lemma 1

For any $i \in [K]$, we have $\mathcal{I}_i=1/2$. Moreover, for any $\bm{\sigma}$ and $S \subseteq [K]$ we have where $m_i=\gamma_i$, $[M]_{ii}=2+\sigma_i^2$, and $[M]_{ij}=\gamma_i \gamma_j$ for all $i , j \in S$ such that $i \neq j$.

Figures (4)

  • Figure 1: A Summary of the Model.
  • Figure 2: The timing of the decisions.
  • Figure 3: Four possible sets $\tilde{\Sigma}_{\bm{a}}$ for $\bm{a} \in \{0,1\}^2$ for a setting with $K=2$ platforms, $\gamma_1=.8$, and $\gamma_2=.7$.
  • Figure 4: Illustrating the point given by \ref{['eqn:equilibrium_K=2']}.

Theorems & Definitions (26)

  • Definition 1: Revealed information
  • Remark 1
  • Lemma 1
  • Lemma 2: monotonicity
  • Lemma 3: submodularity in actions
  • Lemma 4: submodularity in noise variance
  • Proposition 1
  • Lemma 5
  • Proposition 2
  • Lemma 6
  • ...and 16 more