We present an approach to analyse learning outcomes in a broad class of misspecified environments, spanning both single-agent and social learning. We introduce a novel “prediction accuracy” order over subjective models and observe that this makes it possible to partially restore standard martingale convergence arguments that apply under correctly specified learning. Based on this, we derive general conditions to determine when beliefs in a given environment converge to some long-run belief either locally or globally (i.e. from some or all initial beliefs). We show that these conditions can be applied, first, to unify and generalize various convergence results in previously studied settings. Second, they enable us to analyse environments where learning is “slow”, such as costly information acquisition and sequential social learning. In such environments, we illustrate that even if agents learn the truth when they are correctly specified, vanishingly small amounts of misspecification can generate extreme failures of learning.

A multi‐product monopolist faces a buyer who is privately informed about his valuations for the goods. As is well known, optimal mechanisms are in general complicated, while simple mechanisms—such as pure bundling or separate sales—can be far from optimal and do not admit clear‐cut comparisons. We show that this changes if the monopolist has sufficiently precise information about the buyer's valuations: Now, pure bundling always outperforms separate sales; moreover, there is a sense in which pure bundling performs essentially as well as the optimal mechanism. To formalize this, we characterize how fast the corresponding revenues converge to the first‐best revenue as the monopolist's information grows precise: Pure bundling achieves the same convergence rate to the first‐best as optimal mechanisms; in contrast, the convergence rate under separate sales is suboptimal.

We exhibit a natural environment, social learning among heterogeneous agents, where even slight misperceptions can have a large negative impact on long‐run learning outcomes. We consider a population of agents who obtain information about the state of the world both from initial private signals and by observing a random sample of other agents' actions over time, where agents' actions depend not only on their beliefs about the state but also on their idiosyncratic types (e.g., tastes or risk attitudes). When agents are correct about the type distribution in the population, they learn the true state in the long run. By contrast, we show, first, that even arbitrarily small amounts of misperception about the type distribution can generate extreme breakdowns of information aggregation, where in the long run all agents incorrectly assign probability 1 to some fixed state of the world, regardless of the true underlying state. Second, any misperception of the type distribution leads long‐run beliefs and behavior to vary only coarsely with the state, and we provide systematic predictions for how the nature of misperception shapes these coarse long‐run outcomes. Third, we show that how fragile information aggregation is against misperception depends on the richness of agents' payoff‐relevant uncertainty; a design implication is that information aggregation can be improved by simplifying agents' learning environment. The key feature behind our findings is that agents' belief‐updating becomes “decoupled” from the true state over time. We point to other environments where this feature is present and leads to similar fragility results.

We study robust welfare comparisons of learning biases (misspecified Bayesian and some forms of non-Bayesian updating). Given a true signal distribution, we deem one bias more harmful than another if it yields lower objective expected payoffs in all decision problems. We characterize this ranking in static and dynamic settings. While the static characterization compares posteriors signal by signal, the dynamic characterization employs an “efficiency index” measuring how fast beliefs converge. We quantify and compare the severity of several well-documented biases. We also highlight disagreements between the static and dynamic rankings, and that some “large” biases dynamically outperform other “vanishingly small” biases.

We formulate a model of social interactions and misinferences by agents who neglect assortativity in their society, mistakenly believing that they interact with a representative sample of the population. A key component of our approach is the interplay between this bias and agents’ strategic incentives. We highlight a mechanism through which assortativity neglect, combined with strategic complementarities in agents’ behavior, drives up action dispersion in society (e.g., socioeconomic disparities in education investment). We also suggest that the combination of assortativity neglect and strategic incentives may be relevant in understanding empirically documented misperceptions of income inequality and political attitude polarization.

Which information structures are more effective at eliminating first- and higher-order uncertainty and hence at facilitating efficient play in coordination games? We consider a learning setting where players observe many private signals about the state. First, we characterize multiagent learning efficiency, that is, the rate at which players approximate common knowledge. We find that this coincides with the rate at which first-order uncertainty disappears, as higher-order uncertainty vanishes faster than first-order uncertainty. Second, we show that with enough signal draws, information structures with higher learning efficiency induce higher equilibrium welfare. We highlight information design implications for games in data-rich environments.

We propose a class of multiple‐prior representations of preferences under ambiguity, where the belief the decision‐maker (DM) uses to evaluate an uncertain prospect is the outcome of a game played by two conflicting forces, Pessimism and Optimism. The model does not restrict the sign of the DM's ambiguity attitude, and we show that it provides a unified framework through which to characterize different degrees of ambiguity aversion, and to represent the co‐existence of negative and positive ambiguity attitudes within individuals as documented in experiments. We prove that our baseline representation, dual‐self expected utility (DSEU) , yields a novel representation of the class of invariant biseparable preferences (Ghirardato, Maccheroni, and Marinacci (2004)), which drops uncertainty aversion from maxmin expected utility (Gilboa and Schmeidler (1989)), while extensions of DSEU allow for more general departures from independence. We also provide foundations for a generalization of prior‐by‐prior belief updating to our model.

We provide an axiomatic analysis of dynamic random utility, characterizing the stochastic choice behavior of agents who solve dynamic decision problems by maximizing some stochastic process ( U t ) of utilities. We show first that even when ( U t ) is arbitrary, dynamic random utility imposes new testable across‐period restrictions on behavior, over and above period‐by‐period analogs of the static random utility axioms. An important feature of dynamic random utility is that behavior may appear history‐dependent , because period‐ t choices reveal information about U t , which may be serially correlated; however, our key new axioms highlight that the model entails specific limits on the form of history dependence that can arise. Second, we show that imposing natural Bayesian rationality axioms restricts the form of randomness that ( U t ) can display. By contrast, a specification of utility shocks that is widely used in empirical work violates these restrictions, leading to behavior that may display a negative option value and can produce biased parameter estimates. Finally, dynamic stochastic choice data allow us to characterize important special cases of random utility—in particular, learning and taste persistence—that on static domains are indistinguishable from the general model.