Blotto game with testing (the locks, bombs and testing model)

We present a Defense/Attack resource allocation model, where the Defender has some number of 'locks' to protect n vulnerable boxes (sites), and the Attacker is trying to destroy these boxes, having some number of 'bombs' which can be placed into the boxes. Similar models were studied in game theory – e.g. (Colonel) Blotto game, but our model has a feature that is absent in the previous literature. Here, the Attacker tests the vulnerability of all sites before allocating her resources. However, these tests are not perfect, i.e. a test can give a positive result for a box without a lock and a negative result for a box with a lock. We give a full solution for some important special cases of the general Locks-Bombs-Testing (G-LBT) model, where sites have distinct values. These results complement previously known results for a symmetrical LBT model, where all parameters are the same for each box. We also outline an approach to a general solution for the G-LBT model.