  We consider a ridesharing problem where there is uncertainty about the
completion of trips from both drivers and riders. Specifically, we study
ridesharing mechanisms that aim to incentivize commuters to reveal their
valuation for trips and their probability of undertaking their trips. Due to
the interdependence created by the uncertainty on commuters' valuations, we
show that the Groves mechanisms are not ex-post truthful even if there is only
one commuter whose valuation depends on the other commuters' uncertainty of
undertaking their trips. To circumvent this impossibility, we propose an
ex-post truthful mechanism, the best incentive we can design without
sacrificing social welfare in this setting. Our mechanism pays a commuter if
she undertakes her trip, otherwise she is penalized for not undertaking her
trip. Furthermore, we identify a sufficient and necessary condition under which
our mechanism is ex-post truthful.
