Spatio-Temporal Pricing for Ridesharing Platforms
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Ridesharing platforms match drivers and riders to trips, using dynamic prices to balance supply and demand. A challenge is to set prices that are appropriately smooth in space and time, in the sense that drivers will choose to accept their dispatched trips, rather than drive to another area or wait for higher prices or a better trip. We introduce the Spatio-Temporal Pricing (STP) mechanism. The mechanism is incentive-aligned, in that it is a subgame-perfect equilibrium for drivers to accept their dispatches, and the mechanism is welfare-optimal, envy-free, individually rational and budget balanced from any history onward. We work in a complete information, discrete time, multi-period, multi-location model, and prove the existence of anonymous, origin-destination, competitive equilibrium (CE) prices. The STP mechanism employs driver-pessimal CE prices, and the proof of incentive alignment makes use of the M^ concavity of min-cost flow objectives. The same connection to min-cost flow problems provides an efficient algorithm to compute an optimal matching and prices. We also give an impossibility result, that there can be no dominant-strategy mechanism with the same economic properties. An empirical analysis conducted in simulation suggests that the STP mechanism can achieve significantly higher social welfare than a myopic pricing mechanism, and highlights the failure of incentive alignment due to non-smooth prices in myopic mechanisms.
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