Social Optimality and Stability of Matchings in Peer-to-Peer Ridesharing

We propose a socially optimal peer-to-peer ridesharing scheme, where, by contrast to previous literature which considers the total vehicle-kilometres travelled in the objective function, a social planner matches passengers and drivers to maximize social welfare. This amounts to minimize the travel resource costs (travel time and fuel) plus the environmental costs. A linear programming problem is formulated to compute the optimal matchings for networks of any topology. Existence, uniqueness and integrality conditions are investigated. The socially optimal matching solution without environmental costs is proved to satisfy the stability property. The social planner receives a payment from passengers and rewards drivers for the extra costs they bear. Passengers and drivers never incur a loss, but matchings may need to be subsidised. An application to Sioux Falls network illustrates benefits and costs of the scheme for society and the individual participants