We create a general and tractable theory of increasing sorting in pairwise matching models with monetary transfers. The positive quadrant dependence partial order subsumes Becker (1973) as the extreme cases with most and least sorting and implies increasing regression coefficients. Our theory turns on synergy—the cross-partial difference or derivative of match production. This reflects basic economic forces: diminishing returns, technological convexity, insurance, and learning dynamics. We prove sorting increases if match synergy globally increases, and is cross-sectionally monotone or single crossing. We use our results to derive sorting predictions in major economics sorting papers and in new applications.

We characterize the unique equilibrium of a competitive continuous time game between a resource-constrained informed player and a sequence of rivals who partially observe his action intensity. Our game adds noisy monitoring and impatient players to Aumann and Maschler (1966), and also subsumes insider trading models. The intensity bound induces a novel strategic bias and serial mean reversion by uninformed players. We compute the duration of the informed player's informational edge. The uninformed player's value of information is concave if the intensity bound is large enough. Costly obfuscation by the informed player optimally rises in the public deception.