| This dissertation is a collection of three essays that deal with trade-offs that arise in two different dynamic environments: matching and experimentation.;The first two chapters of this thesis develop a theory of stability in dynamic matching markets where (i) matching opportunities arrive over time, (ii) matching is one-to-one, and (iii) matching is irreversible.;In Chapter 1, I propose a stability notion, dynamic stability, which incorporates a backward induction notion to an otherwise cooperative model, which takes into account the time at which the arriving agents can form binding agreements. Dynamically stable matchings may fail to exist in two-sided economies (e.g., adoption markets), and in the allocation of objects with priorities (e.g., public housing). However, dynamically stable matchings always exist in one-sided economies (e.g., deceased-donor organ allocation). The non-existence result reveals a new form of unraveling in matching markets: agents wish to delay the time at which they are matched so as to improve their matching prospects. These findings rationalize why clearing houses in different markets adopt very different rules to deal with the event in which agents reject a current offer to wait for a better match. I also provide sufficient conditions on preferences under which unraveling is prevented.;Chapter 2 expands on the notion of the core developed in Chapter 1 when arrivals are stochastic. This is done by pointing out a connection between a dynamic, two-sided, matching market with stochastic arrivals and a many-to-many matching market. The connection between the environments proves useful to analyze properties of the core using the tools of the many-to-many matching literature. These properties are then used in Chapter 1.;Chapter 3 considers a single agent experimentation problem as in Weitzman. Weitzman's model requires that, conditional on stopping, the agent only takes boxes which have already been inspected. I relax this assumption and allow the agent to take any uninspected box without inspecting its contents when stopping. The analysis proceeds in two steps. First, I provide a partial characterization of the optimal order and stopping policy in the general case. Second, I use the partial characterization, plus assumptions on the prize distributions and inspection costs of the boxes, to characterize the optimal policy. In particular, I find that, under conditions common in the search and information acquisition literature, boxes are inspected following the same order as in Weitzman's rule; however, the stopping rule is different, and I characterize it. |
