Dynamics of Competition in On-Demand Economy : A Differential Games Approach

The viability and success of ride hailing platforms such as Uber, Lyft, depend on how they manage their demand and pool of available drivers. In this paper, we examine how ride hailing platforms can meet demand with supply in a competitive setting where the number of available drivers depends on policies of the platforms; and demand depends on current prices across multiple platforms for the current ride, perceptions of the platforms among their customers, and the expected wait times in different platforms. Prior research has studied the operation of ride hailing platforms with respect to driver dynamics, demand dynamics, and wait times. Our model is different in that we consider (i) competition (i.e., two players are modeled in the game), (ii) time dynamics (i.e., model setting is continuous in time), and (iii) consumers' perception of the platforms in our model along with the aforementioned factors. To the best of our knowledge, our model is unique in considering all of these factors simultaneously. We develop our model in a differential game setup and consider a scenario of duopoly with two platforms. Some of our key findings include: (i) in case of increased demand, whether surge pricing is beneficial for the platforms depends on what stage of the planning horizon the platforms are in and some other characteristics of the platforms, (ii) if the customers become more demanding or sensitive to wait times, both firms become more profitable; however, they do not necessarily increase their prices after the customers become more demanding, and (iii) the platform that has a better initial perception level does not necessarily have higher prices than the other platform. We discuss several other managerial insights from our model and elaborate on the existing business practices