The performance of ridesharing systems is intricately entwined with user participation. To characterize such interplay, we adopt a repeated multi-player, non-cooperative game approach to model a ridesharing platform and its users’ decision-making. Users reveal to the platform their participation preferences over being only riders, only drivers, flexible users, and opt-out based on the expected utilities of each mode. The platform optimally matches users with different itineraries and participation preferences to maximize social welfare. We analytically establish the existence and uniqueness of equilibria and design an iterative algorithm for the solution, for which convergence is guaranteed under mild conditions. A case study is conducted with real travel demand data in Chicago. The results highlight the effect of users’ flexibility regarding mode preferences on system performance (i.e., the average utility of users and the percentage of successful matches). A sensitivity analysis on the level of subsidy and the distribution of utility between matched riders and drivers shows that uneven distributions of utility may lead to a higher percentage of successful matches. Additional insights are provided on the effect of a user's origin and destination locations on their role choice and likelihood to be matched.