  Ride-hailing marketplaces like Uber and Lyft use dynamic pricing, often
called surge, to balance the supply of available drivers with the demand for
rides. We study driver-side payment mechanisms for such marketplaces,
presenting the theoretical foundation that has informed the design of Uber's
new additive driver surge mechanism. We present a dynamic stochastic model to
capture the impact of surge pricing on driver earnings and their strategies to
maximize such earnings. In this setting, some time periods (surge) are more
valuable than others (non-surge), and so trips of different time lengths vary
in the induced driver opportunity cost.
  First, we show that multiplicative surge, historically the standard on
ride-hailing platforms, is not incentive compatible in a dynamic setting. We
then propose a structured, incentive-compatible pricing mechanism. This
closed-form mechanism has a simple form and is well-approximated by Uber's new
additive surge mechanism. Finally, through both numerical analysis and real
data from a ride-hailing marketplace, we show that additive surge is more
incentive compatible in practice than is multiplicative surge.
