Fig. 3: Adoption of ride-sharing decreases with request rate.

In a stylized city topology (panels b–e) users request transportation from a single origin (gray) to destinations in the city periphery homogeneously (results are robust for alternative settings, see Supplementary Note 4). a The global equilibrium adoption of ride-sharing decreases as the number of users increases (blue) while the number of actually shared rides becomes constant (gray). The kink for S = 3 is an artefact related to the small and odd number of requests and matching of exactly two requests per vehicle such that one request can never be paired (see Supplementary Note 3 for details). b–e As the number of users increases, ride-sharing adoption decreases and a sharing/non-sharing pattern emerges around the origin (top), resulting from the equilibrium incentive balance (bottom, illustrated for the numbered destinations) and possible matching constellations. Requests for shared rides are only matched when traveling to the same or to neighboring branches when the combined trip and return is shorter than the sum of individual trips. With few requests (S = 2, panel b), all users request a shared ride. The expected detour and inconvenience is small since it is unlikely to be matched with another user. As the number of users increases (S = 4, panel c), half of the destinations stop sharing in an alternating sharing/non-sharing pattern around the origin. In this configuration, users requesting a shared ride never suffer any detour while users that do not share are disincentivized from doing so due to their high expected detour (compare bottom part of panel c). For high numbers of users (S = 12 and 30, panels d and e), the probability to be matched with another user when requesting a shared ride increases and the financial incentives cannot fully compensate the expected inconvenience. The adoption of ride-sharing decreases until the financial incentives exactly balance the expected inconvenience (panels d and e, bottom). Illustrated here for financial discount ϵ = 0.2 and inconvenience and detour preferences ζ = 0.3 and ξ = 0.3.