This paper explores how autonomous vehicles (AVs) reshape matching efficiency and market power in ride-hailing. Unlike human drivers, AVs operate under centralized algorithms, decoupling service quality from physical fleet size and creating a "capacity paradox". Using a game-theoretic Hotelling model, we analyze market equilibria under independent competition and strategic partnership regimes. We reveal that AV matching efficiency exerts a non-linear impact on capacity and pricing. In competition, high algorithmic precision paradoxically incentivizes the AV platform to shrink its fleet to minimize capital expenditures. In a partnership, the unified platform leverages pricing to either prevent cannibalization or accelerate consumer migration to AVs, contingent on the human-driven fleet's cost-effectiveness. This study provides novel insights into platform strategy and the welfare implications of autonomous mobility integration.