  We consider a class of interdependent security games on networks where each
node chooses a personal level of security investment. The attack probability
experienced by a node is a function of her own investment and the investment by
her neighbors in the network. Most of the existing work in these settings
considers players who are risk-neutral. In contrast, studies in behavioral
decision theory have shown that individuals often deviate from risk-neutral
behavior while making decisions under uncertainty. In particular, the true
probabilities associated with uncertain outcomes are often transformed into
perceived probabilities in a highly nonlinear fashion by the users, which then
influence their decisions. In this paper, we investigate the effects of such
behavioral probability weightings by the nodes on their optimal investment
strategies and the resulting security risk profiles that arise at the Nash
equilibria of interdependent network security games. We characterize graph
topologies that achieve the largest and smallest worst case average attack
probabilities at Nash equilibria in Total Effort games, and equilibrium
investments in Weakest Link and Best Shot games.
