We study a problem of sequential learning and choosing from a group of similar alternatives. The unknown payoff of accepting an alternative depends on a set of common features that enable transfer learning across the group. There is also an idiosyncratic value that needs to be learned by sampling over time. The problem is whether to accept the current alternative, continue sampling, or switch to the next one. We model it as a Bayesian dynamic program and analyze structural properties.

We consider the prototypical problem of sequentially assigning jobs to workers at a large centralized matching platform under an infinite worker supply governed by a fixed distribution; this encapsulates the defining characteristic of large market settings such as online labour marketplaces. The goal is to maximize cumulative payoffs from matches. We resolve several foundational questions pertaining to the complexity of this problem setting and provide novel rate-optimal algorithms and analyses.

In many contexts such as technology and management consulting, clients seek the expertise of providers to find solutions for their business problems. We develop a dynamic game-theoretic model where the provider chooses how to present alternative solutions, and the client chooses which solution to try.