Technical Summary: Fostering Data Collaboration in Digital Transportation Marketplaces

Problem Statement

The rapid expansion of big data in transportation has created a critical need for collaboration between Municipal Authorities (MAs) and Mobility Providers (MPs), such as ride-hailing companies. While data collaboration can significantly enhance traffic state estimation, control, and routing, it is often hindered by privacy concerns. Stakeholders fear that sharing raw data (e.g., trajectories) may leak sensitive customer mobility patterns or reveal operational secrets (e.g., fleet sizes, algorithmic parameters).

Existing privacy-preserving mechanisms, such as encryption-based techniques (e.g., secure multi-party computation), are often computationally intensive and unsuitable for large-scale data sharing. Perturbation-based techniques (e.g., Differential Privacy) offer a trade-off between privacy and utility but introduce data distortion. A critical gap exists in understanding how these perturbation-based mechanisms influence the strategic decision-making of transportation stakeholders. Specifically, it is unclear how the degradation of data quality caused by privacy mechanisms affects the willingness of MPs to share data and the subsequent utility of MAs, particularly in a setting where stakeholders' decisions are interdependent.

Methodology

The paper proposes a game-theoretic framework to model data collaboration in a Business-to-Government (B2G) digital transportation marketplace.

1. Game-Theoretic Framework

The interaction is modeled as a Stackelberg game:

• Leader (MA): The data requester sets the data request specifications, specifically the data quality threshold ($d_k$) and the observation function ($F_{\sigma_k}$).
• Followers (MPs): The data owners respond by deciding whether to share data ($a_k \in \{0,1\}$) and, if sharing, selecting a privacy budget ($\epsilon_k$) for a perturbation-based mechanism.
• Utility Functions:
  • MPs: Maximize a utility function balancing transport-related welfare gains (derived from system improvements) against privacy costs (weighted by $\beta_k$ and the privacy budget $\epsilon_k$).
  • MA: Maximizes transport-related welfare based on the aggregated, perturbed data received from participating MPs.

2. Privacy-Preserving Mechanism

The study focuses on perturbation-based mechanisms, specifically utilizing Differential Privacy (DP).

• Adjacency Definitions: The paper defines two types of adjacency: trajectory-level (removing one vehicle's trajectory) and count-level (removing a batch of trajectories).
• Mechanism Design: A Gaussian mechanism is employed to perturb key statistics (aggregated FoQ trajectory points) required for traffic demand estimation. The mechanism adds noise scaled by the sensitivity of the query function to satisfy $(\epsilon, \delta)$-DP guarantees.
• Integration with LWR Theory: The perturbed data is used within the Lighthill–Whitham–Richards (LWR) traffic flow theory to estimate arrival flows, which are then used to optimize fixed-time traffic signal plans (cycle length, green splits, and offsets).

3. Equilibrium Analysis

The authors analyze the existence and properties of the Stackelberg-Nash Equilibrium (SNE):

• Follower Game: The interaction among MPs is analyzed as a non-cooperative game. The paper establishes conditions for the existence of a unique Nash Equilibrium in the lower stage (given participation decisions) and discusses the submodularity of the upper-stage binary game.
• Collaboration Conditions: Theoretical analysis derives sufficient conditions for successful collaboration, showing that collaboration is more likely when the MA's data quality expectations are moderate or low, allowing MPs to choose privacy budgets that balance utility and privacy costs.

4. Numerical Experiments

A case study based on a real-world arterial network in Hangzhou, China, validates the theoretical findings. The experiment simulates a scenario with one MA and two MPs (each with 20% market penetration) collaborating to optimize traffic signals. The study evaluates the utilities of all stakeholders under varying data quality requirements ($d$) and privacy budgets ($\epsilon$).

Key Contributions

1. Game-Theoretic Framework: The paper introduces a novel Stackelberg game model that explicitly incorporates perturbation-based privacy-preserving mechanisms into the data-sharing strategies of transportation stakeholders.
2. Theoretical Analysis: It provides a rigorous analysis of the equilibrium existence and derives sufficient conditions for successful data collaboration, highlighting the trade-offs between data quality requirements and privacy incentives.
3. Practical Instantiation: The framework is instantiated in a specific transportation application: collaborative traffic signal optimization. The authors design a differentially private traffic demand estimation mechanism that integrates DP with LWR theory to estimate queue front trajectories.
4. Managerial Insights: Numerical studies demonstrate that lower data quality expectations from the MA can incentivize voluntary data sharing. By relaxing strict accuracy requirements, MAs can encourage MPs to participate with higher privacy protection, ultimately improving overall transport welfare.

Results and Findings

• Impact of Data Quality Expectations: The numerical results indicate that excessively high data quality expectations (requiring high $\epsilon$, i.e., low privacy protection) lead to collaboration failure. MPs find the privacy costs too high relative to the utility gains and opt out. Conversely, moderate or low data quality expectations allow MPs to select privacy budgets that yield positive net utility, fostering collaboration.
• Diminishing Marginal Utility: The utility of an MP increases with the privacy budget (accuracy) of other participating MPs, but this benefit exhibits diminishing marginal returns.
• Equilibrium Behavior: The study identifies equilibrium points where the MA achieves maximum utility given the MPs' best responses. In these equilibria, the MA often benefits from accepting slightly distorted data to ensure participation, rather than demanding perfect data that results in zero sharing.
• Privacy-Utility Trade-off: The Gaussian mechanism successfully protects trajectory and count-level privacy while preserving sufficient statistical utility for traffic signal optimization.

Significance and Claims

The paper claims to be among the first to investigate the role of privacy-preserving mechanisms in fostering data collaboration among multiple transportation stakeholders (MAs and MPs) within a B2G marketplace. It bridges the gap between individual-level privacy studies and system-level stakeholder dynamics.

The authors assert that their work provides actionable insights for policymakers and system designers. Specifically, they argue that privacy-preserving technologies can bridge data silos not by eliminating privacy concerns, but by allowing stakeholders to control the level of data distortion. The findings suggest that a "sweet spot" exists where relaxed data quality requirements can incentivize voluntary sharing, leading to improved social welfare and service quality without compromising critical privacy boundaries. The paper positions itself as a methodological pioneer in advancing the understanding of privacy-aware, collaborative transportation systems.