Modern, technologically-enabled markets are disrupting many industry sectors, including transportation, labor, lodging, dating services and others. While the system operator is able to collect data and deploy various control levers, these systems are highly complex, marked by a large number of interacting self-interested agents, uncertainty about the future and imperfect demand predictions. There remain major challenges in optimizing these marketplaces. In this dissertation, I describe work designing novel algorithms and performing theoretical analysis of networked systems, including those that arise in marketplaces. I demonstrate how to use tools from applied probability, modern optimization, and economics to develop methodologies for online decision making in contexts such as queueing control, revenue management, and running a matching platform.
The first part of the dissertation designs novel algorithms for dynamic assignment and revenue management. The work considers networked systems where agents or tasks arrive over time, which is broadly relevant to service platforms with heterogeneous services, for instance shared transportation systems. Firstly, we propose a near optimal ``mirror backpressure'' control methodology for joint entry/assignment/pricing control in a network where there are a fixed number of supply units (vehicles), and demands with different origin and destination nodes arrive over time. The MBP policy does not need demand arrival rate predictions at all, and we prove guarantees of near optimal performance over a finite horizon. Secondly, we study a special case of the network control problem where the geographical imbalances in demand are small enough such that, ignoring stochasticity, they can be corrected using assignment control alone.
The objective is to minimize the fraction of customers who are ``lost'' (not served) because there is no vehicle at a nearby location when the customer arrives. We show that for this setting we can achieve a refined notion of optimality, i.e., the large deviations optimality.
The second part of the dissertation analyzes equilibria in matching markets under different mechanisms. Firstly, we study the Gale-Shalpley ``deferred acceptance'' algorithm, which has been successfully adopted in contexts such as school choice and resident matching programs. Our research question is, ``Which Gale-Shapley matching markets exhibit a short-side advantage?'' I.e., in which markets does being on the short side of the market allow agents to obtain better match partners relative to a similar ``balanced'' market with equal numbers of agents on the two sides? We address this problem by looking at the ``random matching market'' model where each agent considers only a subset of potential partners on the other side, and sharply characterize the resulting (nearly unique) stable matching, overcoming significant technical challenges. Secondly, we study the waiting-list mechanism, which is commonly used in kidney assignment, public housing allocation, and beyond. We show that the waiting-list mechanism is near-optimal in terms of allocative efficiency for general systems with an arbitrary number of agent types and item types, and obtain tight bound on the efficiency loss. Comparing to existing works which could only analyze very simple systems, we tackle the general case by taking a completely different approach and establishing a novel connection with stochastic gradient descent.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/d8-y52c-8t28 |
| Date | January 2021 |
| Creators | Qian, Pengyu |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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