  We explore a scenario involving two sites and a sequential game between a
defender and an attacker, where the defender is responsible for securing the
sites while the attacker aims to attack them. Each site holds a loss value for
the defender when compromised, along with a probability of successful attack.
The defender can reduce these probabilities through security investments at
each site. The attacker's objective is to target the site that maximizes the
expected loss for the defender, taking into account the defender's security
investments. While previous studies have examined security investments in such
scenarios, our work investigates the impact of bounded rationality exhibited by
the defender, as identified in behavioral economics. Specifically, we consider
quantal behavioral bias, where humans make errors in selecting efficient (pure)
strategies. We demonstrate the existence of a quantal response equilibrium in
our sequential game and analyze how this bias affects the defender's choice of
optimal security investments. Additionally, we quantify the inefficiency of
equilibrium investments under quantal decision-making compared to an optimal
solution devoid of behavioral biases. We provide numerical simulations to
validate our main findings.
