Isaac Sonin, UNC Charlotte

*Title: * Locks-Bombs-Testing Model

*Abstract*: I will discuss a very general 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 games, but our model has a feature that is absent from the previous literature. Here, the Attacker tests the vulnerability of all sites before allocating her resources. These tests are not perfect and a test can give a positive result for a box without a lock and a negative result for a box with a lock. I will describe the full solution for several special cases and will discuss a possible approach to a solution for the general case. The only prerequisite for this talk is knowledge of the Total Probability formula and Bayes’ formula.