Natural interviewing equilibria in matching settings

A common assumption in matching markets is that both sides fully know their preferences. However, when there are many participants this may be neither realistic nor feasible. Instead, agents may have some partial (perhaps stochastic) information about alternatives and will invest time and resources to better understand the inherent benefits and tradeoffs of different choices. Using the framework of matching medical residents with hospital programs, we study strategic behaviour by residents in a setting where hospitals maintain a publicly known master list of residents (i.e., all hospitals have an identical ranking of all the residents, for example, based on grades) and residents have to decide with which hospitals to interview, before submitting their preferences to the matching mechanism. We first show the existence of pure strategy equilibrium under very general conditions. We then study the setting when residents' preferences are drawn from a known Mallows distribution. We prove that assortative equilibrium (k top residents interview with k top hospitals, etc.) arises only when residents interview with a small number of programs. Surprisingly, such equilibria (or even weaker notions of assortative interviewing) do not exist when residents can interview with many hospital programs, even when residents' preferences are very similar. Simulations on possible outcome equilibrium indicate that some residents will pursue a reach/safety strategy.