Research

In a model inspired by neuroscience, we study choice between lotteries as a process of encoding and decoding noisy perceptual signals. The implications of this process for behavior depend on the decision-maker's understanding of risk. When the aggregation of perceptual signals is coarse, encoding and decoding generate behavioral risk attitudes even for vanishing perceptual noise. We show that the optimal encoding of lottery rewards is S-shaped and that low-probability events are optimally oversampled. Taken together, the model can explain adaptive-risk attitudes and probability weighting, as in prospect theory. Furthermore, it predicts that risk attitudes are influenced by the anticipation of risk, time pressure, experience, salience, and availability heuristics.

Evidence suggests that consumers do not perfectly optimize, contrary to a critical assumption of classical consumer theory. We propose a model in which consumer types can vary in both their preferences and their choice behavior. Given data on demand and the distribution of prices, we identify the set of possible values of the consumer surplus based on minimal rationality conditions: every type of consumer must be no worse off than if they either always bought the good or never did. We develop a procedure to narrow the set of surplus values using richer data sets and provide bounds on counterfactual demands.

This article investigates the role of private information in patent races. Although prior work assumes that firms observe their rivals' progress, R&D is often conducted in secrecy. We analyze how the race dynamics change when progress is private and examine whether voluntary disclosure is strategically beneficial, even without direct payoff consequences. We show that a firm may disclose its breakthrough to discourage a rival's R&D effort, but only when the rival has not yet done so and R&D efficiency is sufficiently low. The unique equilibrium takes one of three forms: no-revelation, instant-revelation, or mixed-revelation.

We examine the trade-off between patenting and secrecy in innovation races, considering a model where two firms simultaneously compete in developing two products. Patenting ensures a claim on the product but discloses information to the rival, while secrecy may delay immediate profits in exchange for future technology leadership. In the general case, we find that firms have more incentives to patent when they become less patient or when technological spillovers are lower. Furthermore, we compare patenting behavior when the goods are substitutes or complements. When R&D spillovers are small and the firms are not moderately patient, they exhibit a greater tendency to patent products acting as perfect complements rather than perfect substitutes. These findings are in line with the empirical evidence by Cohen, Nelson, and Walsh (2000), who argue that firms are more likely to keep the innovation secret in “simple” industries, where goods have many potential substitutes, as opposed to “complex” industries, where a new product involves many complementary components.

Frontier AI labs spend tens of billions of dollars a year training models whose capabilities an open-weight fringe reproduces within months and then sells at marginal compute cost. Can the frontier labs ever turn a profit? I set out a small dynamic model of that race: a leader's earnings ride the value gap over a competitive open-weight fringe, while its model-building bill tracks the compute path. At the baseline calibration, break-even never arrives — coverage, earnings per dollar of model-building spend, falls over time. Whether that verdict can be overturned becomes a quantitative race among a compute slowdown, accelerating (AI-assisted) algorithmic progress, the shape of the value curve, and two catch-up channels: methods diffusion and distillation of released models. A companion interactive explorer implements the full model in the browser, with calibration sources and a Monte Carlo forecasting mode.