Modeling multi-target defender-attacker games with quantal response attack strategies

Due to the growing interest in incorporating behavioral models within the defender-attacker game literature, the perfect rationality assumption of adversaries has been relaxed in many recent works. This paper studies four multi-target defensive resource allocation in defender-attacker games by using a quantal response model, in which the attacker might be bounded rational. We compare the results from the proposed models with the traditional game theoretic model where the attacker behaves rationally. Moreover, we studied the impacts of the attacker’s rationality level on the defender’s optimal defense strategies. Real data from the Urban Areas Security Initiative (UASI) and the Global Terrorism Database (GTD) are employed to estimate the rationality parameter as well as numerically illustrate the model. The results show that: (a) in the quantal response model, the defender’s expected loss at equilibrium increases with the attacker’s rationality parameter and the expected loss approach the results from the game theoretic model; (b) when the attacker’s rationality parameter in the quantal response model approaches infinity, both the equilibrium defensive allocation and expected loss approach to the results from the game theoretic model; (c) when the attacker uses quantal response while the defender falsely believes that the attacker uses game theoretic response, the expected loss will be similar to the model where both players utilize game theoretic response, but higher than the expected loss from the model where both players use quantal response; (d) when the attacker uses game theoretic response while the defender falsely believes that the attacker uses quantal response, the expected equilibrium loss will be higher than the ones from the other three scenarios; and (e) the quantal response model gives a closer resource allocation to the real allocation than the game theoretic model does. This paper provides some novel insights to defensive resource allocation when considering that the attacker is bounded rationality.