We present a Defense/Attack resource allocation model, where Defenders have some number of "locks" to protect n vulnerable boxes (sites), and attackers are trying to destroy these boxes, having m "bombs" that can be placed into boxes. Similar models were studied in game theory - (Colonel) Blotto games, but our model has a feature absent in previous literature. Attackers test the vulnerability of all sites before allocating their resources, and these tests are not perfect, i.e., a test can give plus for a box without a lock and minus for a box with a lock. We describe the optimal strategies in two versions of this Locks-Bombs-Testing (LBT) model. The inspiration for this model was the paper by K. Sonin, J. Wilson, A. Wright: Rebel Capacity, Intelligence Gathering, and the Timing of Combat Operations (manuscript, 2018).
A small part of my talk will be devoted to a seemingly simple question: what does it mean that two events are independent ? The last time I gave a talk at your University, I mentioned that if we flip a fair coin and a fair die, then the total number of pairs of independent events is 888, 888.