In today’s era of information explosion, decision-makers are faced with a vast amount of information, not all of which is relevant to their decisions. To better make optimal decisions in data-rich environments, the Rational Inattention (RI) model has been introduced into the field of economics. The core idea of this model is that decision-makers need to allocate attention based on the “salience” of information to reduce unnecessary information processing costs. However, traditional RI models assume that decision-makers fully rely on a subjective prior distribution, which may be biased in practical applications, especially when there is uncertainty about the prior distribution.

This paper aims to address this issue by proposing a Robust Rational Inattention model based on prior uncertainty. By allowing decision-makers to have ambiguity aversion regarding the prior distribution, the authors seek to construct a more robust decision-making framework to deal with potential misspecifications of the prior distribution. This robustness not only enhances the reliability of decisions but also better explains real-world decision behaviors.

Paper Source

This paper is co-authored by Lars Peter Hansen, Jianjun Miao, and Hao Xing. Lars Peter Hansen is from the Economics Department and Booth School of Business at the University of Chicago. Jianjun Miao is from the School of Economics at Zhejiang University and the Department of Economics at Boston University. Hao Xing is from the Finance Department at Boston University’s Questrom School of Business. The paper was published on February 7, 2025, in PNAS (Proceedings of the National Academy of Sciences of the United States of America) as an open-access article.

Research Process and Methods

1. Model Setup

This study first constructs a static model of discrete choice, where the core is the information acquisition and decision optimization of decision-makers facing uncertainty. Specifically, the decision-maker aims to maximize expected utility while considering the cost of information acquisition. Information costs are quantified using Shannon’s Mutual Information, and the deviation of the prior distribution is measured using Relative Entropy.

2. Proposal of the Robust Rational Inattention Problem

In traditional RI models, decision-makers base their decisions on a fixed prior distribution. This study relaxes this assumption, allowing decision-makers to explore different prior distributions and introduces a robustness parameter to control the penalty for deviations from the baseline prior. Specifically, the study proposes a Robust Signal RI Problem, where the decision-maker needs to optimize information acquisition and decision-making under the worst-case scenario.

3. Simplification and Solution of the Optimization Problem

To simplify the problem, researchers transform the information acquisition and decision problem into a choice-based optimization problem. By introducing a conditional probability distribution, researchers unify information costs and decision problems and solve them using numerical methods. Particularly, they design a generalized Arimoto-Blahut algorithm based on the Block Coordinate Descent Algorithm to solve the robust RI problem.

Research Results

1. Characteristics of Robust Decision-Making

The study shows that after introducing the robustness parameter, decision-makers tend to tilt the prior distribution towards more cautious or pessimistic directions. This tilt reflects the decision-maker’s concern about prior uncertainty, making the decision more robust. Specifically, the smaller the robustness parameter, the stronger the decision-maker’s ambiguity aversion, leading to an expansion of the consideration set and more options being considered.

2. Results of Numerical Experiments

Through numerical experiments on consumer choice and investment decision problems, researchers verified the impact of the robustness parameter on decision-making. For example, in consumer choice problems, the smaller the robustness parameter, the larger the choice set, and the decision-maker considers more product options. In investment decision problems, adjustments to the robustness parameter significantly influence the decision-maker’s preferences for different investment options.

Conclusion and Value

The core contribution of this study lies in proposing a Robust Rational Inattention model based on prior uncertainty and validating its effectiveness through theoretical analysis and numerical experiments. This model not only extends the traditional rational inattention framework but also provides a more realistic decision-making tool. In practical applications, this model can help decision-makers make more robust decisions in data-rich environments, especially when there is uncertainty about the prior distribution.

Research Highlights

1. Novel Robustness Framework: This study introduces prior uncertainty into the rational inattention model for the first time, constructing a new robust decision-making framework.
2. Combination of Theory and Numerics: By combining theoretical derivation and numerical experiments, researchers provide both analytical solutions and validate the model’s practicality through specific cases.
3. Broad Application Value: This model is not only applicable to the field of economics but can also be extended to statistics, control theory, and other disciplines, offering broad application prospects.

Other Valuable Information

Researchers also point out that future studies can further expand this model, such as introducing a dynamic decision framework or considering uncertainty in the information acquisition process. Additionally, how to apply this model to empirical research, particularly testing its predictive power under prior ambiguity, is another direction worth exploring.