Ride sharing enhances transportation cost-sharing and improves vehicle utilization, offering mutual benefits to both drivers and passengers within the sharing economy. However, existing approaches often overlook the self-interested and rational behaviors of both parties, where drivers aim to maximize income and passengers seek to minimize costs. To address this gap, we model dynamic ride sharing as a many-to-one matching game, where drivers and passengers rank each other based on preference metrics with constraints. We introduce an Enhanced Matrix-based Ant Colony Optimization (EMACO) algorithm for real-time path estimation and a Continuous Two-Sided Matching (CTSM) algorithm to dynamically match drivers and passengers while ensuring Pareto-optimal, stable outcomes. We validate our approach using real-world taxi GPS trajectory datasets from Beijing, Guangzhou, and New York. Experimental results show that our proposed algorithms outperform existing baselines in key performance metrics.