The Effect of Behavioral Probability Weighting in a Sequential Defender-Attacker Game

We consider a setting consisting of two sites, and a sequential game between a defender and an attacker who are responsible for securing and attacking the sites, respectively. Each site has a value to the defender, and an associated probability of successful attack, which can be reduced via security investments in that site by the defender. The attacker targets the site that maximizes the expected loss for the defender (after the investments). While prior work has studied the security investments in such scenarios, in this work we consider what happens when the defender exhibits characteristics of bounded-rationality that have been identified by behavioral economics. In particular, humans have been shown to perceive probabilities in a nonlinear manner, typically overweighting low probabilities and underweighting high probabilities. We characterize how such nonlinear probability weighting affects the security investments made by the defender, and bound the inefficiency of the equilibrium investments under behavioral decision-making, compared to a non-behavioral optimal solution.