Too Good to Fire: Non-Assortative Matching to Play a Dynamic Game

We study stable outcomes in a one-to-one matching market with firms and workers. The model endogenizes how transferable utility is within a match: when a firm-worker pair is matched, they play an infinite-horizon discounted dynamic game with one-sided, observable effort. Partners’ types are complementary in determining the maximal feasible payoffs. In our setting, the classic result that with complementary types stable matchings are positively assortative does not hold. Increasing the quality of a match harms dynamic incentives, because a firm cannot credibly threaten to fire a worker who is productive even with low effort. Thus, firms may prefer lower-type workers who will exert more effort. Our analysis suggests a new interpretation of efficiency wages: committing to pay a high wage can improve effort incentives indirectly by making the firm more willing to walk away.