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Incentive Design for Ridesharing with Uncertainty

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.