Carpooling is often promoted as a mode to reduce traffic congestion and vehicle miles traveled in road networks. This project develops a game-based mode-choice model for the morning commute involving carpooling supported by a ridesharing platform. In the model, commuters travel from homesin the suburb (Origin) to offices in downtown (Destination) either driving alone or carpooling. A ridesharing platform provides ride-matching services to carpoolers. Carpoolers riding in one vehicle can equally share the shareable travel costs among them but will be charged matching fees by the ridesharing platform. We assume all commuters attempt to minimize their own generalized commuting costs, and derive the evolutionarily stable states (ESS) and social optimum (SO) state by using replicator dynamics and by minimizing the average generalized costs, respectively. Under ESS and SO states, we analyzed the effects of high-occupancy-vehicle (HOV) lanes and matching fees on commuters' mode choice and the ridesharing platform's profits. We find that the platform's profit-seeking behavior may increase congestion on general-purpose (GP) lanes and may reduce the efficiency of the overall system. Congestion on GP lanes is more likely to increase when the ratio of HOV capacity to freeway capacity is high, the proportion of shareable travel costs in generalized costs is low, inconvenience costs joining carpools are high, and the platform is profit-seeking. The results of this model show that ridesharing platforms need to be regulated and HOV capacity needs to be carefully allocated in order to make carpool benefit everyone.