Pricing and equilibrium in on-demand ride-pooling markets

With the recent rapid growth of technology-enabled mobility services, ride-sourcing platforms, such as Uber and DiDi, have launched commercial on-demand ride-pooling programs that allow drivers to serve more than one passenger request in each ride. Without requiring the prearrangement of trip schedules, these programs match on-demand passenger requests with vehicles that have vacant seats. Ride-pooling programs are expected to offer benefits for both individual passengers in the form of cost savings and for society in the form of traffic alleviation and emission reduction. In addition to some exogenous variables and environments for ride-sourcing market, such as city size and population density, three key decisions govern a platform's efficiency for ride-pooling services: trip fare, vehicle fleet size, and allowable detour time. An appropriate discounted fare attracts an adequate number of passengers for ride-pooling, and thus increases the successful pairing rate, while an appropriate allowable detour time prevents passengers from giving up ride-pooling service. This paper develops a mathematical model to elucidate the complex relationships between the variables and decisions involved in a ride-pooling market. We find that the monopoly optimum, social optimum and second-best solutions in both ride-pooling and non-pooling markets are always in a normal regime rather than the wild goose chase (WGC) regime—an inefficient equilibrium in which drivers spend substantial time on picking up passengers. Besides, in general, a unit decrease in trip fare in a ride-pooling market attracts more passengers than would a non-pooling market, because it not only directly increases passenger demand due to the negative price elasticity, but also reduces actual detour time, which in turn indirectly increases ride-pooling passenger demand. As a result, we prove that monopoly optimum, social optimum and second-best solution trip fares in a ride-pooling market are lower than that in a non-pooling market under certain conditions. These theoretical findings are further verified by a set of numerical studies.