Protecting Assets with Heterogeneous Valuations under Behavioral Probability Weighting

We consider a security setting involving a defender who is required to invest (subject to a budget constraint) in protecting a given set of nodes against attacks. Each node has a certain value to the defender, along with a probability of being successfully compromised, which is a function of the investment in that node by the defender. In this setting, we consider the impacts of behavioral probability weighting (vis-à-vis the probability of successful attack) 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 that under appropriate conditions on the probability of successful attack, the defender's optimization problem is convex (even under probability weighting). Furthermore, we show that behavioral probability weighting causes the defender to shift more of her investments to the higher-valued nodes and underinvest in the low-value nodes, compared to the case where the defender perceives the probability of attack correctly. In particular, the number of nodes that have positive investment decreases as the defender becomes more behavioral.