A seller sells an object over time but is uncertain how the buyer learns their willingness-to-pay. We consider informational robustness under limited commitment, where the seller offers a price each period to maximize continuation profit against worst-case information arrival. Our formulation considers the worst case sequentially. Under general conditions, we characterize an essentially unique equilibrium. Furthermore, we identify a condition that ensures the equilibrium price path is "reinforcing," so even non-sequentially worst-case information arrival would not lower the seller's payoff below the equilibrium level.

We propose an efficient boosting algorithm for multiclass classification, called AdaBoost.Iter, that extends SAMME and AdaBoost. The algorithm iteratively applies the weak learnability condition of SAMME to eliminate classes to find the correct classificiation. The iterative weak learnability is a sufficient and necessary condition for boostability, but it is also easier to validate than the EOR criterion of AdaBoost.MM \citeMukherjeeSchapire2013. We show that the training error of AdaBoost.Iter vanishes at the exponential rate, while the generalization error converges to zero at the same rate as AdaBoost. AdaBoost.Iter numerically outperforms SAMME and achieves performance comparable to AdaBoost.MM on benchmark datasets.

This paper concerns the design of contracts to incentivize experts to acquire information for predicting a future state when doing so is costly and when this information acquisition is private. This problem may arise in a variety of situations, often when the contract designer expects to make a high-stakes decision---for instance, whether to launch a military attack in response to a perceived threat, whether to make a sizable investment, or whether to approve a risky vaccine to fight a budding pandemic. In these cases, whether a given action is best (e.g., invasion, investment, approval, respectively, for the above examples) may depend on the underlying state, which we will take as binary in this paper for simplicity. Notice that this problem features the combination of moral hazard (since the principal cannot monitor the expert's effort) and endogenous adverse selection (since the expert's actions generate private information).

An agent samples projects over time, observing a binary quality realization for each, while a principal can select at most one. The principal values quality, whereas the agent only wants a project chosen. Transfers are unavailable, but the principal can verify quality by paying a constant fixed cost. We find optimal dynamic mechanisms (i.e., project allocation and verification rules) for this problem. There are three main cases we consider:

We study dynamic disclosure when an exogenous public signal may reflect firm value, but may also reflect pure noise. This departs from past work on this setting, which typically takes the informativeness of the exogenous news to be known. We show that uncertainty over whether the public signal reflects the manager's value creates an asymmetry in the market's interpretation of news; if equilibrium involves pre-emptive disclosure, prices may drop discontinuously as news improves. We contrast these results with what is obtained when the correlation between the public signal and firm value is known and deterministic. The patterns we highlight emerge because higher signals are viewed as less informative---that is, they are taken "with a grain of salt."

We introduce an evolutionary framework to evaluate competing (mis)specifications in strategic situations, focusing on which misspecifications can persist over a correct specification. Agents with heterogeneous specifications coexist in a society and repeatedly match against random opponents to play a stage game. They draw Bayesian inferences about the environment based on personal experience, so their learning depends on the distribution of specifications and matching assortativity in the society. One specification is evolutionarily stable against another if, whenever sufficiently prevalent, its adherents obtain higher expected objective payoffs than their counterparts. The learning channel leads to novel stability phenomena compared to frameworks where the heritable unit of cultural transmission is a single belief instead of a specification (i.e., set of feasible beliefs). We apply the framework to linear-quadratic-normal games where players receive correlated signals but possibly misperceive the information structure. The correct specification is not evolutionarily stable against a correlational error, whose direction depends on matching assortativity. As another application, the framework also endogenizes coarse analogy classes in centipede games. The full paper can be found at https://kevinhe.net/papers/theory_evolution.pdf