  We consider the game with discrete units of resources for protection and
destruction of some sites. In our model, Defender (DF) has locks and Attacker
(AT) has bombs to allocate among sites, trying to destroy these sites. One or
more bombs can be placed into the same site. A site is destroyed if at least
one explosion occurs. A lock is a protection device which, placed in a site,
prevents its destruction with any number of bombs in it. The important feature
of the model is that AT can and will test every site, trying to find sites
without locks. This testing is not perfect: a test of a site may have a
positive result, even if there is no lock at the site, or a negative result,
even if there is a lock. The probabilities of correct identification of both
types (sensitivity and specificity) are known to both players. In the Bayesian
setting we assume that the probability distribution of the locks is known to
AT, although the actual positions of the locks are not. After the locks are
allocated, AT receives the test results, and distributes the bombs among the
sites, trying to maximize the expected sum of values of all destroyed sites.
The goal of DF is to select a prior distribution of locks to minimize this
loss. Some special cases of this game are completely solved, and some partial
results are obtained for the general model.
