The paper provides a characterization of Blackwell-monotone information cost functions, which assign higher costs to more informative statistical experiments according to Blackwell's classical information order.
Key highlights:
For binary experiments, Blackwell monotonicity is equivalent to the cost function being permutation invariant and satisfying certain directional derivative conditions.
For experiments with more than two signals, Blackwell monotonicity is characterized by the cost function being permutation invariant and satisfying a system of linear differential inequalities, along with a quasiconvexity assumption.
For additively separable information cost functions, Blackwell monotonicity is equivalent to the component function being sublinear (positively homogeneous and subadditive). This identifies a broad class of Blackwell-monotone costs, including norm costs, absolute-linear costs, and existing costs like entropy and posterior-separable costs.
The characterizations provide a tractable method to verify Blackwell monotonicity of arbitrary information cost functions and enable the construction of novel Blackwell-monotone costs.
The results are applied to study bargaining and persuasion problems with costly information, showing how the general framework can strengthen existing insights by relaxing additional assumptions.
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by Xiaoyu Cheng... at arxiv.org 04-24-2024
https://arxiv.org/pdf/2404.15158.pdfDeeper Inquiries