A prime example of coopetition in the transportation sector is rental car agencies leasing underutilised fleet vehicles to freelance drivers who provide service through peer-to-peer (P2P) ride-hailing platforms. We adopt and analyse a classic sequential game-theoretic model in which the ride-hailing platform serves as a two-sided market connecting service providers and consumers (riders), while the rental car agency offers leasing contracts to both retail consumers (renters) and latent ride-hailing providers. Existing operations management literature has offered a limited examination of coopetition between two-sided markets with respect to service wait-time sensitivity and capacity constraints on leasing services. We analyse both service wait times and the own-versus-lease decision of heterogeneous providers on the ride-hailing platform to show how coopetition affects all participants in the equilibrium. When high vehicle acquisition costs constrain service capacity, adding ride-hailing providers does not necessarily reduce pre-service wait times. Under coopetition, fares may even rise, potentially harming consumers. On the other hand, even in a market with high service capacity, adding freelance providers through coopetition could still benefit consumers. We also investigate the impact of coopetition on consumer loyalty to suggest when the regulatory authority should encourage or disallow such a collaboration. Rental car companies like Hertz now lease underutilised fleet vehicles to Uber and Lyft drivers, exemplifying coopetition in the transportation sector. While car rental agencies can generate revenue through vehicle leases to freelancing drivers, they risk expanding the ridesharing platform and reducing the demand for car rentals. This study explores when rental agencies can achieve a win-win by sharing service capacity with ride-hailing platforms. In particular, the number of existing and latent drivers serves as a key indicator for assessing potential collaboration. When there are few drivers in a market, the rental platform can generate substantial profits by converting latent drivers to lessee-providers to alleviate the service bottleneck. Vehicle supply shortages resulting from high maintenance and upkeep costs can be mitigated by the rental platform, reinforcing the incentive for cooperation. When short-term leases offered by the rental platform become viable for ride-hailing drivers, both platforms can raise prices and increase profits, as reduced competition allows the rental platform to benefit from ride-hailing revenues. However, more ride-hailing drivers may result in longer wait times for consumers. In markets with many existing drivers, marginal capacity increases may be outpaced by demand growth, actually lengthening delays. As long as ride-hailing platforms maintain a reasonable level of service quality, governments should encourage coopetition among them. Governmental intervention, on the other hand, may be necessary when partnerships benefit platforms at consumers’ expense, such as a market with very few drivers where the service value is too low for consumers to switch from rentals to ride-hailing.