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• Propose a duopoly evolutionary game model for the dynamic ride-hailing market. • Capture bounded rationality, strategic learning, and dynamic competition between platforms. • Identify the existence of stationary points and derive simplified stability conditions. • Establish two extended models to capture the service aggregator and mixed electric/fuel fleets. • Provide a fresh perspective for exploring dynamic ride-hailing competition and market evolution. The platform competition in a real-world ride-hailing market is complex and dynamic. Existing research mainly relies on static competitive equilibrium, lacking an understanding of the dynamic evolution process of platform competition. This paper develops a generic duopoly evolutionary game model to capture dynamic decision adjustments and the evolution of market conditions. Bounded rationality and strategic learning are integrated into the modeling to dissect the interaction and competition between two platforms. The existence of stationary points where the system states remain unchanged over time is identified, and simplified stability conditions are derived. A pure strategy pair is found stable when constituting a strict Nash equilibrium and corresponding to positive payoffs. We establish two extended models to capture the nascent service aggregator and mixed electric/fuel fleets and compare them with the basic model. The model is calibrated employing the ride-hailing data of New York and is applicable for analyzing the market evolution under different states. The impacts of potential demand drop, aggregated services, and mixed fleets on platform decision and driver-passenger choice evolution are unveiled. It is found that the platforms possess self-recovery capability when facing a deteriorated external environment. The decision-making of the small platform exhibits a more substantial inertia and volatility since the large platform's decision can easily influence the market supply and demand. In the initial stage, the service aggregator slightly harms the large platform, but in the long run, it benefits both platforms. Besides, both platforms reduce prices while inflating commission ratios under mixed fleets. This study provides a fresh perspective for exploring the real-world dynamic ride-hailing competition and market evolution. [ABSTRACT FROM AUTHOR]