This paper introduces a general model of matching that includes evolving public Bayesian reputations and stochastic production. Despite productive com-plementarity, assortative matching robustly fails for high discount factors, unlike in (Becker 1973). This failure holds around the highest (lowest) reputation agents for ‘high skill ’ (‘low skill’) technologies. We find that matches of likes eventually dissolve. In another life-cycle finding, young workers are paid less than their marginal product, and old workers more. Also, wages rise with tenure but need not reflect marginal products: Information rents produce non-monotone and discontinuous wage profiles. ∗An earlier version of this was circulated as “Assortative Matching, Reputation, and the Beatles Break-up”. Axel is grateful to the University of Michigan for financial support, while Lones much appreciates continued funding from the NSF. The paper reflects substantive comments of two referees and the Editor, Juuso Valimaki. We wish to thank Ennio Stacchetti specifically for substantial help with the existence proof. We have profited from the comments of two anonymous referees, as well as

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. (JEL C78, D21, D82, D86, J12)

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. (JEL D82, D83, G14)

We develop a continuum player timing game that subsumes standard wars of attrition and pre‐emption games, and introduces a new rushes phenomenon. Payoffs are continuous and single‐peaked functions of the stopping time and stopping quantile. We show that if payoffs are hump‐shaped in the quantile, then a sudden “rush” of players stops in any Nash or subgame perfect equilibrium. Fear relaxes the first mover advantage in pre‐emption games, asking that the least quantile beat the average; greed relaxes the last mover advantage in wars of attrition, asking just that the last quantile payoff exceed the average. With greed, play is inefficiently late: an accelerating war of attrition starting at optimal time, followed by a rush. With fear, play is inefficiently early: a slowing pre‐emption game, ending at the optimal time, preceded by a rush. The theory predicts the length, duration, and intensity of stopping, and the size and timing of rushes, and offers insights for many common timing games.

Do the world’s best tennis pros play Nash equilibrium mixed strategies? We answer this question using data on serve-direction choices (to the receiver’s left, right, or body) from the Match Charting Project. Using a new approach, we test and reject a key implication of a mixed-strategy Nash equilibrium: that the probability of winning the service game is identical for all possible serve strategies. We calculate best-response serve strategies by dynamic programming (DP) and show that for most elite pro servers, the DP strategy significantly increases their win probability relative to the mixed strategies they actually use.