We study learning in a large class of complete information normal form games. Players continually face new strategic situations and must form beliefs by extrapolation from similar past situations. We characterize the long-run outcomes of learning in terms of iterated dominance in a related...

In order to identify expertise, forecasters should not be tested by their calibration score, which can always be made arbitrarily small, but rather by their Brier score. The Brier score is the sum of the calibration score and the refinement score; the latter measures how good the sorting into...

Objects of different quality are to be allocated to agents. Agents can receive at most one object, and there are not enough high-quality objects for every agent. The value to the social planner from allocating objects to any given agent depends on that agent's private information. The social...

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...

A sender designs an information structure to persuade a receiver to take an action. The sender is ignorant about the receiver's prior, and evaluates each information structure using the receiver's prior that is the worst for the sender. I characterize the optimal information structures in this...

Decision theory can be used to test the logic of decision making---one may ask whether a given set of decisions can be justified by a decision-theoretic model. Indeed, in principal-agent settings, such justifications may be required---a manager of an investment fund may be asked what beliefs she...

I consider the interaction between an agent and a principal who is unable to commit not to renegotiate. The agent's type only affects the principal's utility. The principal has access to a public signal, correlated with the agent's type, which can be used to (imperfectly) verify the agent's...

We model an individual who wants to learn about a state of the world. The individual has a prior belief, and has data which consists of multiple forecasts about the state of the world. Our key assumption is that the decision maker identifies explanations that could have generated this data and...

A planner wants to elicit information about an agent's preference relation, but not the entire ordering. Specifically, preferences are grouped into "types", and the planner only wants to elicit the agent's type. We first assume beliefs about randomization are subjective, and show that a space of...

This paper introduces two simple betting mechanisms, Top-Flop and Threshold betting, to elicit unverifiable information from crowds. Agents are offered bets on the rating of an item about which they received a private signal versus that of a random item. We characterize conditions for the chosen...