In this study, we propose an integrated model of two‐sided stochastic matching platforms to understand the design and operations of free‐float shared‐mobility systems. In particular, we address the joint design of incentives (via “crowd‐sourcing”) and spatial capacity allocations (enabled by “geo‐fencing”). From the platform's perspective, we formulate stylized models based on strategic double‐ended queues. We optimize the design and operations of such systems in a case study using a data set from a leading free‐float bicycle‐sharing system, and solve it via mixed‐integer second‐order conic programs (SOCPs). Both stylized results and computational studies generate insights about fundamental trade‐offs and triangular relationships among operational costs, capacity utilization rates and service levels. Interestingly, we identify the role of spatial capacity (parking) management to fine‐tune the market thickness (transient service availability) in such a two‐sided marketplace. We show that a “capacity‐dependent approximation” can be very close to optimality, and outperforms policies ignoring capacity management. We also demonstrate that this framework can be operationalized in multiple directions, which generates insights concerning matching efficiency, performance comparison between crowd‐sourcing and repositioning, strategic server behaviors and network externalities. Our insights guide the platform and the policy‐maker to embrace “crowd‐sourcing” and “geo‐fencing” technologies for shared‐mobility systems.