This paper analyzes the problem of matching heterogenous agents in a Bayesian learning model. One agent gives a noisy signal to another agent, who is responsible for learning. If production has a strong informational component, a phase of cross-matching occurs, so that agents of low knowledge catch up with those of higher one. It is shown that (i) a greater informational component in production makes cross-matching more likely; (ii) as the new technology is mastered, production becomes relatively more physical and less informational; (iii) a greater dispersion of the ability to learn and transfer information makes self-matching more likely; and (iv) self-matching leads to more self-matching, whereas croos-matching can make less productive agents overtake more productive ones.