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Motivated by markets for “expertise,” we study a bandit model where a principal chooses between a safe and risky arm. A strategic agent controls the risky arm and privately knows whether its type is high or low. Irrespective of type, the agent wants to maximize duration of experimentation with the risky arm. However, only the high type arm can generate value for the principal. Our main insight is that reputational incentives can be exceedingly strong unless both players coordinate on maximally inefficient strategies on path. We discuss implications for online content markets, term limits for politicians, and experts in organizations. 

Abstract Different agents need to make a prediction. They observe identical data, but have different models: they predict using different explanatory variables. We study which agent believes they have the best predictive ability—as measured by the smallest subjective posterior mean squared prediction error—and show how it depends on the sample size. With small samples, we present results suggesting it is an agent using a low-dimensional model. With large samples, it is generally an agent with a high-dimensional model, possibly including irrelevant variables, but never excluding relevant ones. We apply our results to characterize the winning model in an auction of productive assets, to argue that entrepreneurs and investors with simple models will be overrepresented in new sectors, and to understand the proliferation of “factors” that explain the cross-sectional variation of expected stock returns in the asset-pricing literature. 

Motivated by their increasing prevalence, we study outcomes when competing sellers use machine learning algorithms to run real-time dynamic price experiments. These algorithms are often misspecified, ignoring the effect of factors outside their control, for example, competitors’ prices. We show that the long-run prices depend on the informational value (or signal-to-noise ratio) of price experiments: if low, the long-run prices are consistent with the static Nash equilibrium of the corresponding full information setting. However, if high, the long-run prices are supra-competitive—the full information joint monopoly outcome is possible. We show that this occurs via a novel channel: competitors’ algorithms’ prices end up running correlated experiments. Therefore, sellers’ misspecified models overestimate the own price sensitivity, resulting in higher prices. We discuss the implications on competition policy. 

We show how to achieve the notion of "multicalibration" from Hébert-Johnson et al. [2018] not just for means, but also for variances and other higher moments. Informally, it means that we can find regression functions which, given a data point, can make point predictions not just for the expectation of its label, but for higher moments of its label distribution as well-and those predictions match the true distribution quantities when averaged not just over the population as a whole, but also when averaged over an enormous number of finely defined subgroups. It yields a principled way to estimate the uncertainty of predictions on many different subgroups-and to diagnose potential sources of unfairness in the predictive power of features across subgroups. As an application, we show that our moment estimates can be used to derive marginal prediction intervals that are simultaneously valid as averaged over all of the (sufficiently large) subgroups for which moment multicalibration has been obtained.