Recent U.S. evidence suggests that the response of the labor share to a productivity shock is characterized by countercyclicality and overshooting. These findings cannot be easily reconciled with existing business cycle models. We extend the standard model of search and matching in the labor market by considering strategic interactions among an endogenous number of producers. This leads to countercyclical price markups. While Nash bargaining is sufficient to capture the labor share countercyclicality, we show that countercyclical markups are key to address the overshooting.