We examine the coopetition relationship between a ride-sharing platform and a car-rental firm. A distinctive aspect of this coopetition relationship is that they operate under two different business models. The platform, exploiting information technology (IT) capabilities, controls its demand and supply sides by setting rider price and driver wage in real time based on demand and supply conditions. In contrast, the car-rental firm operates under the traditional model with a fixed supply and cost structure. Both the IT-driven platform and the car-rental firm compete for riders seeking for transportation. If the two engage in coopetition, they cooperate to allow a (secondary) driver to rent from the rental firm and drive for the platform. In the absence of coopetition, only those with their own vehicles (i.e., primary drivers) are allowed to drive for the platform. We show that such supply-side (i.e., driver-side) cooperation intensifies the demand-side (i.e., rider-side) price competition and decreases total revenue. Therefore, coopetition is mutually beneficial only when it leads to a significant decrease in the supply, or driver, cost. Moreover, when coopetition is mutually beneficial, the benefit arises solely because of the improved profit margin from riders who switch from the rental firm to the platform and from those who are switched from primary to secondary drivers. We find that the platform and the rental firm are likely to form a coopetition relationship when the total rider market size is not high, the degree of rider substitutability between the platform and the rental firm is low, or the platform has a significant market-size advantage over the rental firm. Coopetition between the platform and the rental firm benefits riders and hurts drivers, but benefits society overall. The incentive to form the coopetition relationship is enhanced if cross-side network effects are present on the platform or if each player serves a loyal rider segment in addition to the competitive rider segment that considers the two as substitutes.