Matching While Learning

Platforms face a cold start problem whenever new users arrive: namely, the platform must learn attributes of new users (explore) in order to match them better in the future (exploit). How should a platform handle cold starts when there are limited quantities of the items being recommended? For instance, how should a labor market platform match workers to jobs over the lifetime of the worker, given a limited supply of jobs? In this setting, there is one multiarmed bandit problem for each worker, coupled together by the constrained supply of jobs of different types. A solution is developed to this problem. It is found that the platform should estimate a shadow price for each job type, and for each worker, adjust payoffs by these prices (i) to balance learning with payoffs early on and (ii) to myopically match them thereafter.