Carpooling is recognized as a viable alternative by city managers to reduce traffic demand and consequent congestion and pollution on city roads. Members of a carpool face the daily challenge of deciding whether to go alone or with some or all members of their carpool, and further, to take their own vehicle or ride with others. These decisions may seem trivial in isolation but if not taken judiciously, over time, may disrupt the carpool. In this paper, we have designed a system which models daily carpool scheduling as a repeated stochastic game played among willing carpoolers which allows for individual choices and promotes carpooling as an equilibrium outcome through equitable payoff distribution using social credits. We empirically show the efficacy of our system through simulation and also discuss how game-theoretic design inherently helps to deploy the system as a mobile application.