Perfect information with potentially negative value: An intriguing war story and a possible explanation

When the Allies were bombing Germany in World War II, it is rumoured that before certain raids they would let the Germans know, without realizing the information was leaked on purpose, that one of the potential targets would not be attacked. While this information was correct and taken as such, the Germans have allegedly made additional erroneous inferences from it, rendering their overall defensive alignment less effective than before the information was leaked. This note attempts to ‘explain’ this scenario via a resource allocation model which minimizes expected damage. The key issues is whether the subjective probability of a particular site is significantly lower after receiving the information than the corresponding pre-information probability. This issue seems of interest in its own right, and could also be relevant in modern strategic business settings. Some related behavioural issues are discussed.