We fully solve a sorting problem with heterogeneous firms and multiple heterogeneous workers whose skills are imperfect substitutes. We show that optimal sorting, which we call mixed and countermonotonic, is comprised of two regions. In the first region, mediocre firms sort with mediocre workers and coworkers such that the output losses are equal across all these teams (mixing). In the second region, a high-skill worker sorts with low-skill coworkers and a high-productivity firm (countermonotonicity). We characterize the equilibrium wages and firm values. Quantitatively, our model can generate the dispersion of earnings within and across US firms.

Using a natural experiment from a retail gasoline antitrust case, we study how asymmetric information sharing affects oligopoly pricing. Empirically, price competition softens when, following case settlement, information sharing shifts from symmetric to asymmetric, with one firm losing access to high-frequency granular rival price data. We provide theory and empirics illustrating how strategic ignorance creates price commitment, leading to higher price-cost margins. Using a structural model, we find substantial profit-enhancing effects of asymmetric information sharing. These results provide a cautionary tale for antitrust agencies regarding the potential unintended consequences of limiting price information sharing among firms.