Reputation, learning and project choice in frictional economies

I introduce a dynamic model of learning and random meetings between a long-lived agent with unknown ability and heterogeneous projects with observable qualities. The outcomes of the agent’s matches with the projects determine her posterior belief about her ability (i.e., her reputation). In a self-type learning framework with endogenous outside option, I find the optimal project selection strategy of the agent, that determines what types of projects the agent with a certain level of reputation will accept. Sections of the optimal matching set become increasing intervals, with different cutoffs across different types of the projects. Increasing the meeting rate has asymmetric effects on the sections of the matching sets: it unambiguously expands the section for the high type projects, while on some regions, it initially expands and then shrinks the section of the low type projects.