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Autonomous vehicles will be an integral part of ride-sharing services in thefuture. This setting differs from traditional ride-sharing marketplaces becauseof the absence of the supply side (drivers). However, it has far-reachingconsequences because in addition to pricing, players now have to make decisionson how to distribute fleets across network locations and re-balance vehicles inorder to serve future demand. In this paper, we explore a duopoly setting inthe ride-sharing marketplace where the players have fully autonomous fleets.Each ride-service provider (RSP)'s prices depend on the prices and the supplyof the other player. We formulate their decision-making problems using agame-theoretic setup where each player seeks to find the optimal prices andsupplies at each node while considering the decisions of the other player. Thisleads to a scenario where the players' optimization problems are coupled and itis challenging to find the equilibrium. We characterize the types of demandfunctions (e.g.: linear) for which this game admits an exact potential functionand can be solved efficiently. For other types of demand functions, we proposean iterative algorithm to compute the equilibrium. We conclude by providingnumerical insights into how different kinds of equilibria would play out in themarket when the players are asymmetric. Our numerical evaluations also provideinsights into how the regulator needs to consider network effects whiledeciding regulation in order to avoid unfavorable outcomes.

Pricing in Ride-sharing Markets : Effects of network competition and autonomous vehicles