Information Acquisition and Time-Risk Preference

TL;DR

This paper models an agent's dynamic information acquisition process with strategies that optimize the dispersion of threshold-hitting times, revealing how beliefs evolve as a compensated Poisson process under different strategies.

Contribution

It introduces a framework for analyzing information acquisition strategies based on time risk, including explicit strategies that maximize or minimize this dispersion.

Findings

Beliefs follow a compensated Poisson process under both strategies.

The greedy strategy jumps beliefs to the closer threshold in Bregman divergence.

The pure accumulation strategy maintains constant entropy during belief jumps.

Abstract

An agent acquires information dynamically until her belief about a binary state reaches an upper or lower threshold. She can choose any signal process subject to a constraint on the rate of entropy reduction. Strategies are ordered by "time risk"-the dispersion of the distribution of threshold-hitting times. We construct a strategy maximizing time risk (Greedy Exploitation) and one minimizing it (Pure Accumulation). Under either strategy, beliefs follow a compensated Poisson process. In the former, beliefs jump to the threshold that is closer in Bregman divergence. In the latter, beliefs jump to the unique point with the same entropy as the current belief.