We propose a restrictiveness measure for economic models based on how well they fit pre-defined synthetic data. This measure, together with a measure for how well the model fits real data, outlines a Pareto frontier, where models that rule out more regularities, yet capture the regularities that are present in real data, are preferred. To illustrate our approach, we evaluate the restrictiveness of models in two laboratory settings—certainty equivalents and initial play—and one field setting—takeup of microfinance in Indian villages. The restrictiveness measure reveals insights about each, including that some economic models with only a few parameters are very flexible.

We propose a tractable unified framework to study the evolution and interaction of model-misspecification concerns and complexity aversion in repeated decision problems. This aims to capture environments where decision makers worry that their models are misspecified while also disliking overly complex models. We find that pathological cycles caused by endogenous concerns for misspecification can be eliminated by penalizing complex models and show that such preferences for simplicity tend to favor safety, which can enhance welfare in the long run. We use our framework to provide new microfoundations for pervasive empirical phenomena such as "scale heterogeneity" in discrete-choice analysis, "probability neglect" in behavioral economics, and "home bias" in international finance.

We generalize the notion of model restrictiveness in Fudenberg, Gao and Liang (2026) to a wider range of economic models with semi/non-parametric and structural ingredients. We show how restrictiveness can be defined and computed in infinite-dimensional settings using Gaussian process priors (including with shape restrictions) and other alternativess in Bayesian nonparametrics. We also extend the restrictiveness framework to structural models with endogeneity, instrumental variables, multiple equilibria, and nonparametric nuisance components. We discuss the importance of the user-specific choice of discrepancy functions in the context of Rademacher complexity and GMM criterion function, and relate restrictiveness to the limit of the average-case learning curve in machine learning. We consider applications to: (1) preferences under risk, (2) exogenous multinomial choice, and (3) multinomial choice with endogenous prices: for (1), we obtain results consistent with those in Fudenberg, Gao and Liang (2026); for (2) and (3), our findings show that nested logit and mixed logit exhibit similar restrictiveness under standard parametric specifications, and that IV exogeneity conditions substantially increase overall restrictiveness while altering model rankings.

We study R D competition in the shadow of disaster: advancing the technology frontier raises the risk of permanently ending all firms' payoffs. Under perfect monitoring and common knowledge of rationality, the equilibrium frontier is bounded below by the optimal stopping time of a monopolist, and above by that of a representative firm that persistently but mistakenly believes its rival is about to stop. We then analyze how the frontier is shaped by transparency (speed of monitoring) and trust (belief in the rationality of rival firms).

A sender first publicly commits to an experiment and then can privately run additional experiments and selectively disclose their outcomes to a receiver. The sender has private information about the maximal number of additional experiments they can perform (i.e., their type). We show that the sender cannot attain their commitment payoff in any equilibrium if (i) the receiver is sufficiently uncertain about their type and (ii) the sender could benefit from selective disclosure after conducting their full-commitment optimal experiment. Otherwise, there can be equilibria where the sender obtains their commitment payoff.

Economists often estimate models using data from a particular domain, e.g. estimating risk preferences in a particular subject pool or for a specific class of lotteries. Whether a model's predictions extrapolate well across domains depends on whether the estimated model has captured generalizable structure. We provide a tractable formulation for this "out-of-domain" prediction problem and define the transfer error of a model based on how well it performs on data from a new domain. We derive finite-sample forecast intervals that are guaranteed to cover realized transfer errors with a user-selected probability when domains are iid, and use these intervals to compare the transferability of economic models and black box algorithms for predicting certainty equivalents. We find that in this application, the black box algorithms we consider outperform standard economic models when estimated and tested on data from the same domain, but the economic models generalize across domains better than the black-box algorithms do.

AI systems have the potential to improve decision-making, but decision makers face the risk that the AI may be misaligned with their objectives. We study this problem in the context of a treatment decision, where a designer decides which patient attributes to reveal to an AI before receiving a prediction of the patient's need for treatment. Providing the AI with more information increases the benefits of an aligned AI but also amplifies the harm from a misaligned one. We characterize how the designer should select attributes to balance these competing forces, depending on their beliefs about the AI's reliability. We show that the designer should optimally disclose attributes that identify rare segments of the population in which the need for treatment is high, and pool the remaining patients.

We study the impact of endogenous attention in a dynamic social media model. Each period, a user observes a random story and decides whether to share it. Users like sharing true and interesting stories, but identifying false stories requires costly attention. Depending on parameters, the system exhibits either a unique limit or strong path dependence. Endogenous attention responds to changes in false story credibility, so reducing credibility can boost their prevalence. Increases in the exogenous production rate of false stories can be amplified by users' sharing decisions. Increasing users' capacity to reach others amplifies both true and false stories; we identify conditions under which the net effect favors truth over falsehood.

We study community enforcement in a large population with noisy monitoring. We focus on equilibria in the prisoner's dilemma that are coordination proof, meaning that matched partners never play a Pareto-dominated Nash equilibrium in the one-shot game induced by the equilibrium continuation payoffs at their current histories. We show that a noise-tolerant version of contagion strategies is optimal among all coordination-proof equilibria. Welfare under tolerant contagion strategies decreases in the noise level and the gain from defection faster than welfare in a fixed partnership does. Thus, community enforcement has a comparative advantage in supporting "low-stakes"relationships. ( JEL C72, C73, C78, Z13)

We study agents who are more likely to remember some experiences than others, but who update their beliefs as if the experiences they remember are the only ones that occurred. Long-run behavior is characterized by selective memory equilibrium where people choose actions that maximize their payoff given their distorted recollection of the outcomes. We show how this captures the effects of many biases from the literature. We also study the long-run outcomes when the expected number of recalled experiences is bounded and if an experience is recalled it is more likely to be recalled again, and agents who are only partially na¨ıve about their selective memory. Jehiel, Koster, Oprea,

This note discusses functions over lotteries that are concave and continuous, but are not necessarily superdifferentiable. Earlier work claims that concave continuous utility for lotteries that satisfy best-outcome independence can be written as the minimum of affine functions. We give a counter-example that cannot be written as the minimum of affine functions, because there is no tangent hyperplane that dominates the functions at the boundary. We then review the fact that concavity and upper semi-continuity are equivalent to a representation as the infimum of affine functions, and show that these assumptions imply continuity for functions on finite-dimensional lotteries. Therefore, in finite-dimensional simplices, concavity and continuity are equivalent to the “infimum” representation. The “minimum” representation is equivalent to the existence of local utilities (supporting affine functions) at every lottery, a property that is equivalent to superdifferentiability.

We use simulations of a simple learning model to predict cooperation rates in the experimental play of the indefinitely repeated prisoner’s dilemma. We suppose that learning and the game parameters only influence play in the initial round of each supergame, and that after these rounds, play depends only on the outcome of the previous round. We find that our model predicts out-of-sample cooperation at least as well as models with more parameters and harder-to-interpret machine learning algorithms. Our results let us predict the effect of session length and help explain past findings on the role of strategic uncertainty. (JEL C57, C72, C73, D83, D91)

We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback–Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman's (1990) uniform convergence result to, e.g., priors that have finite support, are constrained by independence assumptions, or have a parametric form that cannot match some probability distributions. The concentration result lets us provide a rate of convergence for Berk's (1966) result on the limiting behavior of posterior beliefs when the prior is misspecified. We provide a bound on approximation errors in “anticipated‐utility” models, and extend our analysis to outcomes that are perceived to follow a Markov process.

We use an evolutionary model to determine which misperceptions can persist. Every period, a new generation of agents use their subjective models and the data generated by the previous generation to update their beliefs, and models that induce better actions become more prevalent. An equilibrium can resist mutations that lead agents to use a model that better fits the equilibrium data but induce the mutated agents to take an action with lower payoffs. We characterize which steady states resist mutations to a nearby model, and which resist mutations that drop a qualitative restriction such as independence.

We show that the treatment effect estimated by standard methods such as regression discontinuity analysis or difference-in-differences may contain a transient “learning effect” that is entangled with the long-term effect of the treatment. This learning effect occurs when the variable of interest is the agents’ efforts, when treatment and control correspond to success or failure: success or failure gives agents information about how much their effort matters, and consequently changes the amount of effort they provide after treatment. We examine the impact of the learning effect and when it is likely to be substantial. (JEL C13, C21, D72, D74, D83, I20)

We present a speculative application of model estimates from Fudenberg and Puri (2021) to prize-linked savings in South Africa. The models used include one combining simplicity theory (Puri 2018, 2022), a preference for lotteries with fewer possible outcomes, with cumulative prospect theory. The results and those of prior literature indicate that both simplicity and probability weighting have a role to play in understanding behavior in choice under risk. We discuss the properties of these models and their implications for behavior.

Economic models are evaluated by testing the correctness of their predictions. We suggest an additional measure, “completeness”: the fraction of the predictable variation in the data that the model captures. We calculate the completeness of prominent models in three problems from experimental economics: assigning certainty equivalents to lotteries, predicting initial play in games, and predicting human generation of random sequences. The completeness measure reveals new insights about these models, including how much room there is for improving their predictions.

We analyze situations in which players build reputations for honesty rather than for playing particular actions. A patient player facing a sequence of short-run opponents makes an announcement about their intended action after observing an idiosyncratic shock, and before players act. The patient player is either an honest type whose action coincides with their announcement, or an opportunistic type who can freely choose their actions. We show that the patient player can secure a high payoff by building a reputation for being honest when the short-run players face uncertainty about which of the patient player's actions are currently feasible, but may receive a low payoff when there is no such uncertainty.

Learning models do not in general imply that weakly dominated strategies are irrelevant or justify the related concept of “forward induction,” because rational agents may use dominated strategies as experiments to learn how opponents play, and may not have enough data to rule out a strategy that opponents never use. Learning models also do not support the idea that the selected equilibria should only depend on a game's reduced normal form. However, playing the extensive form of a game is equivalent to playing the normal form augmented with the appropriate terminal node partitions so that two games are information equivalent, i.e., the players receive the same feedback about others' strategies.