Strategic transmission of imperfect information: why revealing evidence (without proof) is difficult - Manuel Foerster (International Journal of Game Theory, 2023)
In our cheap-talk setting, an expert privately observes multiple binary signals, her soft evidence, about a continuous state of the world and then communicates with a decision-maker. While direct transmission of evidence entails communicating the underlying signals, indirect transmission of evidence entails communicating a summary statistic of her evidence. We first establish that fully informative equilibria exist if the conflict of interest is small. Otherwise, direct transmission of evidence is impossible, as withholding one part of the soft evidence in the communication necessarily induces incentives to manipulate the report on the other part. On the contrary, indirect transmission of evidence remains partially informative for intermediate conflicts of interest. Finally, we introduce the possibility of certification. We show that, if the costs of certification are low, the expert can fully reveal her evidence regardless of the conflict of interest.
Keywords: C72; D82; D83; 330; Cheap talk; Soft evidence; Imperfect information; Strategic communication; Certification