Harmful Signaling in Matching Markets

Several labor markets, including the job market for new Ph.D. economists, have recently developed formal signaling mechanisms. We show that such mechanisms are harmful for some environments. While signals transmit previously unavailable information, they also facilitate information asymmetry that leads to coordination failures. In particular, we consider a two-sided matching game of incomplete information between firms and workers. Each worker has either the same "typical" known preferences with probability close to one or "atypical" idiosyncratic preferences with the complementary probability close to zero. Firms have known preferences over workers. We show that under some technical condition if at least three firms are responsive to some worker's signal, the introduction of signaling strictly decreases the expected number of matches