  Motivated by the rapid development of autonomous vehicle technology, this
work focuses on the challenges of introducing them in ride-hailing platforms
with conventional strategic human drivers. We consider a ride-hailing platform
that operates a mixed fleet of autonomous vehicles (AVs) and conventional
vehicles (CVs), where AVs are fully controlled by the platform and CVs are
operated by self-interested human drivers. Each vehicle is modelled as a Markov
Decision Process that maximizes long-run average reward by choosing its
repositioning actions. The behavior of the CVs corresponds to a large game
where agents interact through resource constraints that result in queuing
delays. In our fluid model, drivers may wait in queues in the different regions
when the supply of drivers tends to exceed the service demand by customers. Our
primary objective is to optimize the mixed AV-CV system so that the total
profit of the platform generated by AVs and CVs is maximized. To achieve that,
we formulate this problem as a bi-level optimization problem OPT where the
platform moves first by controlling the actions of the AVs and the demand
revealed to CVs, and then the CVs react to the revealed demand by forming an
equilibrium that can be characterized by the solution of a convex optimization
problem. We prove several interesting structural properties of the optimal
solution and analyze simple heuristics such as AV-first where we solve for the
optimal dispatch of AVs without taking into account the subsequent reaction of
the CVs. We propose three numerical algorithms to solve OPT which is a
non-convex problem in the platform decision parameters. We evaluate their
performance and use them to show some interesting trends in the optimal AV-CV
fleet dimensioning when supply is exogenous and endogenous.
