  We present two zero-sum games modeling situations where one player attacks
(or hides in) a finite dimensional nonempty compact set, and the other tries to
prevent the attack (or find him). The first game, called patrolling game,
corresponds to a dynamic formulation of this situation in the sense that the
attacker chooses a time and a point to attack and the patroller chooses a
continuous trajectory to maximize the probability of finding the attack point
in a given time. Whereas the second game, called hiding game, corresponds to a
static formulation in which both the searcher and the hider choose
simultaneously a point and the searcher maximizes the probability of being at
distance less than a given threshold of the hider.
