  This paper investigates the impacts of competition in autonomous
mobility-on-demand systems. By adopting a network-flow based formulation, we
first determine the optimal strategies of profit-maximizing platform operators
in monopoly and duopoly markets, including the optimal prices of rides.
Furthermore, we characterize the platform operator's profits and the consumer
surplus. We show that for the duopoly, the equilibrium prices for rides have to
be symmetric between the firms. Then, in order to study the benefits of
introducing competition in the market, we derive universal theoretical bounds
on the ratio of prices for rides, aggregate demand served, profits of the
firms, and consumer surplus between the monopolistic and the duopolistic
setting. We discuss how consumers' firm loyalty affects each of the
aforementioned metrics. Finally, using the Manhattan network and demand data,
we quantify the efficacy of static pricing and routing policies and compare it
to real-time model predictive policies.
