We study large-population repeated games where players are symmetric but not anonymous, so player-specific rewards and punishments are feasible. Players may be commitment types who always take the same action. Even though players are not anonymous, we show that an anti-folk theorem holds when...

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 bins with...

This paper generalizes the concept of Bayes' correlated equilibrium Bergemann and Morris (2016) to multistage games. We apply our characterization results to a number of illustrative examples and applications.

This paper studies a game of attack and interception in a network where a single attacker chooses a target and a path, and each node chooses a level of protection. We show that the Nash equilibrium of the game exists and is unique. We characterize equilibrium attack paths and attack...

We study contracting when both principal and agent have to exert noncontractible effort for production to take place. An analyst is uncertain about what actions are available and evaluates a contract by the expected payoffs it guarantees to each party in spite of the surrounding uncertainty....

We study a receiver's learning problem of choosing an informative test in a signaling environment. Each test induces a signaling subgame. Thus, in addition to its direct effect on the receiver's information, a test has an indirect effect through the sender's signaling strategy. We show that the...

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...

I study endogenous learning dynamics for people who misperceive intertemporal correlations in random sequences. Biased agents face an optimal-stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws are...

We consider a moral hazard problem in which a principal provides incentives to a team of agents to work on a risky project. The project consists of two milestones of unknown feasibility. While working unsuccessfully, the agents' private beliefs regarding the feasibility of the project decline....

In a general interdependent preference environment, we characterize when two payoff types can be distinguished by their rationalizable strategic choices without any prior knowledge of their beliefs and higher order beliefs. We show that two payoff types are strategically distinguishable if and...