Autonomous ride-hailing platforms, such as Waymo and Cruise, are quickly expanding their services, but their interactions with the existing ride-hailing companies, such as Uber and Lyft, are rarely discussed. To fill this gap, this paper focuses on the competition between an emerging autonomous ride-hailing platform and a traditional ride-hailing platform by characterizing the equilibrium of their competition and the impact of technology transfer. In particular, we consider an autonomous ride-hailing platform that owns the AV technology and offers ride-hailing services to passengers through a fleet of AVs. In the meanwhile, it competes with a traditional ride-hailing platform that primarily relies on a fleet of human-driver vehicles (HDVs) but may rent a sub-fleet of AVs from the autonomous ride-hailing platform to complement the human-driver fleet (referred to as AV technology transfer). A game-theoretic model is formulated to characterize the competition between the autonomous ride-hailing platform and the traditional ride-hailing platform over a transportation network, encapsulating the passengers' mode choices, the drivers' job options, the network traffic flows and the strategic decisions of the platforms. An algorithm is proposed to compute the approximate Nash equilibrium of the game and conduct an ex-post evaluation on the performance of the obtained solutions. The proposed framework and solution algorithm are validated through a realistic case study for Manhattan. Based on numerical simulations, we find that technology transfer of AVs between the two platforms can lead to a win-win situation where both two platforms get a higher profit, but this comes at the cost of reduced surpluses for human drivers and passengers. In the simulation, a critical trade-off is revealed for the autonomous ride-hailing platform: it strategically forfeits some of its market share in ride-hailing services to encourage the traditional ride-hailing platform to rent more AVs, thereby increasing its rental revenue and consequently, the overall profit. Furthermore, we also find it intriguing that as AV technology improves and operational costs decrease, the traditional ride-hailing platform cannot enjoy any benefit in its profit although it has the option of leasing AVs from the autonomous ride-hailing platform at lower operational costs. Instead, it is compelled to rent a larger fleet of AVs from the autonomous ride-hailing platform at a higher rental price, consequently suffering a reduced profit. Conversely, the autonomous ride-hailing platform significantly benefits from the reduced AV operational cost by capturing a larger market share in the ride-hailing market and earning higher revenue from the AV technology transfer. • Investigated the competition between autonomous and traditional ride-hailing platforms. • A game-theoretic model to capture the incentives of players over transportation networks. • An algorithm is proposed to obtain an approximate Nash equilibrium. • Examined the impacts of AVs on traditional ride-hailing market under platform competition. [ABSTRACT FROM AUTHOR]