Blackwell-Monotone Information Costs

A Blackwell-monotone information cost function assigns higher costs to Blackwell more informative experiments. This paper provides simple necessary and sufficient conditions for a cost function to be Blackwell monotone over finite experiments. The key condition involves a system of linear differential inequalities. By using this characterization, we show that when a cost function is additively separable, it is Blackwell monotone if and only if it is the sum of sublinear functions. This identifies a wide range of practical information cost functions. Finally, we apply our results to bargaining and persuasion problems with costly information, broadening and strengthening earlier findings.