Optimal Dynamic Information Acquisition

Abstract

I study a dynamic model in which a decision‐maker (DM) acquires information about the payoffs of different alternatives prior to making a decision. The model's key feature is the flexibility of information: the DM can choose any dynamic signal process as an information source, subject to a flow cost that depends on the informativeness of the signal. Under the optimal policy, the DM acquires a signal that arrives according to a Poisson process. The optimal Poisson signal confirms the DM's prior belief and is sufficiently precise to warrant immediate action. Over time, given the absence of the arrival of a Poisson signal, the DM continues seeking an increasingly precise but less frequent Poisson signal.

Time Lotteries and Stochastic Impatience

“…Since β t is convex in t, the latter option is preferred whenever E[t] = t. Note that the curvature of the utility function over prizes plays no role in this comparison. This aspect of the standard model has important implications, with many papers relying crucially and explicitly on it (e.g., Ely and Szydlowski (2020), Zhong (2019)). 2 As the standard model makes such sharp predictions, we start our investigation by testing them in incentivized experiments.…”

“…Note that the curvature of the utility function over prizes plays no role in this comparison. This aspect of the standard model has important implications, with many papers relying crucially and explicitly on it (e.g., Ely and Szydlowski (), Zhong ())…”

“… For example, Zhong () studies dynamic models of information acquisition and shows that the optimal strategy uses Poisson signals. The reason is that the decision time with Poisson signals is a mean‐preserving spread of the decision time in any other strategy, and is thus preferred under EDU due to RSTL. …”

“…If instead uncertainty resolved gradually over time, the absence of risk could improve planning. We want to separate this instrumental benefit from intrinsic preferences.2 For example,Zhong (2019) studies dynamic models of information acquisition and shows that the optimal strategy uses Poisson signals. The reason is that the decision time with Poisson signals is a mean-preserving spread of the decision time in any other strategy, and is thus preferred under EDU due to RSTL.…”

Slow persuasion

“…Viscosity solutions of differential equations were introduced by Crandall and Lions (1983). We give a brief exposition and some references in supplemental Appendix K. Viscosity methods have begun to be used in economic theory (e.g., Nikandrova and Pancs (2018), Ke and Villas‐Boas (2019), Keller and Rady (2020), Zhong (2022) and Barilla and Gonçalves (2022)). Our sender's best‐reply problem is nonstandard due the discontinuities in her flow payoff and her ability to freeze the state variable (the public belief), precluding off‐the‐shelf use of standard results.…”