  We consider a security game in a setting consisting of two players (an
attacker and a defender), each with a given budget to allocate towards attack
and defense, respectively, of a set of nodes. Each node has a certain value to
the attacker and the defender, along with a probability of being successfully
compromised, which is a function of the investments in that node by both
players. For such games, we characterize the optimal investment strategies by
the players at the (unique) Nash Equilibrium. We then investigate the impacts
of behavioral probability weighting on the investment strategies; such
probability weighting, where humans overweight low probabilities and
underweight high probabilities, has been identified by behavioral economists to
be a common feature of human decision-making. We show via numerical experiments
that behavioral decision-making by the defender causes the Nash Equilibrium
investments in each node to change (where the defender overinvests in the
high-value nodes and underinvests in the low-value nodes).
