Learning-Based Pricing and Matching for Two-Sided Queues
Zixian Yang Lei Ying
We consider a dynamic system with multiple types of customers and servers.
Each type of waiting customer or server joins a separate queue, forming a
bipartite graph with customer-side queues and server-side queues. The platform
can match the servers and customers if their types are compatible. The matched
pairs then leave the system. The platform will charge a customer a price
according to their type when they arrive and will pay a server a price
according to their type. The arrival rate of each queue is determined by the
price according to some unknown demand or supply functions. Our goal is to
design pricing and matching algorithms to maximize the profit of the platform
with unknown demand and supply functions, while keeping queue lengths of both
customers and servers below a predetermined threshold. This system can be used
to model two-sided markets such as ride-sharing markets with passengers and
drivers. The difficulties of the problem include simultaneous learning and
decision making, and the tradeoff between maximizing profit and minimizing
queue length. We use a longest-queue-first matching algorithm and propose a
learning-based pricing algorithm, which combines gradient-free stochastic
projected gradient ascent with bisection search. We prove that our proposed
algorithm yields a sublinear regret $\tilde{O}(T^{5/6})$ and queue-length bound
$\tilde{O}(T^{2/3})$, where $T$ is the time horizon. We further establish a
tradeoff between the regret bound and the queue-length bound:
$\tilde{O}(T^{1-\gamma/4})$ versus $\tilde{O}(T^{\gamma})$ for $\gamma \in (0,
2/3].$