Profit-aware graph framework for cross-platform ride-sharing: Analyzing allocation mechanisms and efficiency gains

Ride-sharing has the potential to reduce travel costs and VMT by increasing vehicle occupancy. However, fragmentation across competing ride-hailing companies confines shared trips within individual platforms, limiting system-wide efficiency gains. Overcoming this barrier requires fair and incentive-compatible profit allocation mechanisms. This study proposes a profit-aware collaborative framework to evaluate how collaboration under different profit allocation mechanisms influences the feasibility and performance of cross-platform ride-sharing. The proposed framework embeds profit-aware constraints directly into the rider matching process. This allows profit considerations to shape feasible cross-platform matches while ensuring that collaboration remains beneficial for all participating platforms. Within this framework, we evaluate three representative allocation mechanisms—equal-profit-based, market-share-based, and Shapley-value-based—through large-scale simulations calibrated to realistic conditions. Results indicate that collaboration improves system efficiency, including higher share rates, reduced waiting times, and lower VMT. Among the evaluated mechanisms, the Shapley-value-based allocation achieves the most balanced improvements in overall system performance and platform profits. We further find that efficiency gains increase with demand density, reflecting economies of scale (EOS) in shared mobility systems, although marginal benefits diminish as sharing opportunities become saturated. These findings provide quantitative insights into how profit-sharing design can support sustainable cross-platform collaboration and improve urban mobility efficiency in increasingly competitive ride-hailing markets.