Equilibria of bilateral taxi-customer searching and meeting on networks

This paper proposes an equilibrium model to characterize the bilateral searching and meeting between customers and taxis on road networks. A taxi driver searches or waits for a customer by considering both the expected searching or waiting time cost and ride revenue, and a customer seeks a taxi ride to minimize full trip price. We suppose that the bilateral taxi-customer searching and meeting occurs anywhere in residential and commercial zones or at prescribed taxi stands, such as an airport or a railway station. We propose a meeting function to spell out the search and meeting frictions that arise endogenously as a result of the distinct spatial feature of the area and the taxi-customer moving decisions. With the proposed meeting function and the assumptions underlying taxi-customer search behaviors, the stationary competitive equilibrium achieved at fixed fare prices is determined when the demand of the customers matches the supply of taxis or there is market clearing at the prevailing searching and waiting times in every meeting location. We establish the existence of such an equilibrium by virtue of Brouwer's fixed-point theorem and demonstrate its principal operational characteristics with a numerical example.