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 (1990)'s...

We study learning and information acquisition by a Bayesian agent whose prior belief is misspecified in the sense that it assigns probability 0 to the true state of the world. At each instant, the agent takes an action and observes the corresponding payoff, which is the sum of a fixed but...

A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived. Each buyer has private information about his arrival time and valuation where the latter evolves according to a geometric Brownian motion. Any incentive-compatible mechanism has to induce...

We study information design with multiple privately informed agents who interact in a game. Each agent's utility is linear in a real-valued state. We show that there always exists an optimal mechanism which is laminar partitional and bound its ``complexity''. For each type profile, such a...

We establish convergence of beliefs and actions in a class of one-dimensional learning settings in which the agent's model is misspecified, she chooses actions endogenously, and the actions affect how she misinterprets information. Our stochastic-approximation-based methods rely on two crucial...

We establish convergence of beliefs and actions in a class of one‐dimensional learning settings in which the agent's model is misspecified, she chooses actions endogenously, and the actions affect how she misinterprets information. Our stochastic‐approximation‐based methods rely on two...

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...

We study models of learning in games where agents with limited memory use social information to decide when and how to change their play. When agents only observe the aggregate distribution of payoffs and only recall information from the last period, aggregate play comes close to Nash...

We define and analyze a "strategic topology'' on types in the Harsanyi-Mertens-Zamir universal type space, where two types are close if their strategic behavior is similar in all strategic situations. For a fixed game and action define the distance between a pair of types as the difference...

This paper proposes the solution concept of interim correlated rationalizability, and shows that all types that have the same hierarchies of beliefs have the same set of interim-correlated-rationalizable outcomes. This solution concept characterizes common certainty of rationality in the...