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<p>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.</p><p>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.</p><p>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.</p>
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