This paper investigates the Bayesian decision-theoretic foundations of the Wall Street adage that `timing is everything'. One might think that a `small' risk-neutral trader wishes to act immediately upon any private information he possesses. I begin with a counterintuitive nding that trade timing doesn't matter for an Arrow security, as one's expected return per dollar invested is a martingale. This timing irrelevance discovery motivates an analysis of general compound securities. While timing there is ambiguous, I nd that natural monotone likelihood ratio assumptions on both private and public information restore the intuition that one should trade with all due dispatch.(This abstract was borrowed from another version of this item.)

Consider a heterogeneous agent matching model in which the payoff of each matched individual is a fixed function of both partners' types. In a 1973 article, Becker showed that assortative matching arises in a frictionless setting simply if everyone prefers higher partners. This paper shows that if finding partners requires time-consuming search and individuals are impatient, then productive interaction matters. Matching is positively assortative—higher types match with higher sets of types—when the proportionate gains from having better partners rise in one's type. With multiplicatively separable payoffs, these proportionate gains are constant in one's type, and "block segregation" arises, a common finding of the literature.

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 develop a strategic theory of counterfeiting as a multi-market large game. Bad guys choose whether to counterfeit, and what quality to produce. Opposing them is a continuum of good guys who select a costly verification effort. In equilibrium, counterfeiters produce better quality at higher notes, but verifiers try sufficiently harder that verification still improves. We develop a graphical framework for deducing comparative statics. Passed and counterfeiting rates vanish for low and high notes. Our predictions are consistent with time series and cross-sectional patterns in a unique data set assembled largely from the Secret Service.

We introduce and solve a new class of “downward-recursive” static portfolio choice problems. An individual simultaneously chooses among ranked stochastic options, and each choice is costly. In the motivational application, just one may be exercised from those that succeed. This often emerges in practice, such as when a student applies to many colleges or when a firm simultaneously tries several technologies. We show that such portfolio choice problems quite generally entail maximizing a submodular function of finite sets—which is NP-hard in general. Still, we show that a greedy algorithm finds the optimal set, finding first the best singleton, then the best single addition to it, and so on. We show that the optimal choices are “less aggressive” than the sequentially optimal ones, but “more aggressive” than the best singletons. Also, the optimal set in general contains gaps. We provide some comparative statics results on the chosen set.

In Becker's (1973) neoclassical marriage market model, matching is positively assortative if types are complements: i.e., match output f(x, y) is suipermoddlar in x and y. We reprise this famous result assuming time-intensive partner search and transferable output. We prove existence of a search equilibrium with a continuum of types, and then characterize matching. After showing that Becker's conditions on match output no longer suffice for assortative matching, we find sufficient conditions valid for any search frictions and type distribution: supermodularity not only of output f, but also of log f, and log f Symmetric submodularity conditions imply negatively assortative matching. Examples show these conditions are necessary.

This paper explores how Bayes-rational individuals learn sequentially from the discrete actions of others. Unlike earlier informational herding papers, we admit heterogeneous preferences. Not only may type-specific ‘herds’ eventually arise, but a new robust possibility emerges: confounded learning. Beliefs may converge to a limit point where history offers no decisive lessons for anyone, and each type's actions forever nontrivially split between two actions. To verify that our identified limit outcomes do arise, we exploit the Markov-martingale character of beliefs. Learning dynamics are stochastically stable near a fixed point in many Bayesian learning models like this one.

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.