Peer-to-peer (P2P) sharing marketplaces enable sharing of idle resources. When a renter requests an owner’s resource, the owner needs to decide whether to accept the request: accepting it helps the owner fill up the idle periods of the resource and generate a payoff but reduces the flexibility to serve a future request for a longer duration. This paper develops a framework to uncover the tradeoffs faced by owners on these platforms when making acceptance decisions, which can be used by owners to optimize their decisions and by platforms to improve their operations. The model explicitly accommodates two types of owners: some are attentive to the availability states of their cars and forward-looking, whereas others myopically make the acceptance decisions. Applying the model to unique data from a leading peer-to-peer car sharing platform in China, we obtain similar sizes of both types of owners and find that female, experienced, and younger owners are more likely to be strategic. The results also reveal the differentiated preferences of the two types of owners toward their renters. Building on model estimates, we calibrate the option value of each day in the future (i.e., the value of having the day available) for strategic owners and find it to first increase, then decrease. Two counterfactual analyses are conducted. The first analysis shows that if the platform imposes a minimum rental duration, strategic owners may become more reluctant to accept requests, even if the current availability state entails a higher expected payoff. The second analysis shows that with better understanding of its owners, the platform can greatly improve the matching efficiency by optimal (re)allocation of rental requests, a move that benefits almost all participants in the business.