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Interdependent Security Games on Networks under Behavioral Probability Weighting

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.