Stochastic Optimization in Market Design and Incentive Management Problems
This dissertation considers practical operational settings, in which a decision maker needs to either coordinate preferences or to align incentives among different parties. We formulate these issues into stochastic optimization problems and use a variety of techniques from the theories of applied probability, queueing and dynamic programming.
First, we study a stochastic matching problem. We consider matching over time with short and long-lived players who are very sensitive to mismatch, and propose a novel method to characterize the mismatch. In particular, players' preferences are uniformly distributed on a circle, so the mismatch between two players is characterized by the one-dimensional circular angle between them. This framework allows us to capture matching processes in applications ranging from ride sharing to job hunting. Our analytical framework relies on threshold matching policies, and is focused on a limiting regime where players demonstrate low tolerance towards mismatch. This framework yields closed-form optimal matching thresholds. If the matching process is controlled by a centralized social planner (e.g. an online matching platform), the matching threshold reflects the trade-off between matching rate and matching quality. The corresponding optimal matching threshold is smaller than myopic matching threshold, which helps building market thickness. We further compare the centralized system with decentralized systems, where players decide their matching partners. We find that matching controlled by either side of the market may achieve optimal social welfare.
Second, we consider a dynamic incentive management problem in which a principal induces effort from an agent to reduce the arrival rate of a Poisson process of adverse events. The effort is costly to the agent, and unobservable to the principal, unless the principal is monitoring the agent. Monitoring ensures effort but is costly to the principal. The optimal contract involves monetary payments and monitoring sessions that depend on past arrival times. We formulate the problem as a stochastic optimal control model and solve the problem analytically. The optimal schedules of payment and monitoring demonstrate different structures depending on model parameters. Overall, the optimal dynamic contracts are simple to describe, easy to compute and implement, and intuitive to explain.
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