Defender–Attacker Games with Asymmetric Player Utilities

The presence of strategic attackers has become an important factor in the security and protection of systems, especially since the 9/11/2001 attacks, and considerable efforts have been dedicated to its study. When defending against the strategic attacker, many existing studies assume that the attacker would seek to minimize the defender's utility, which implies that the defender and attacker have symmetric utilities. However, the attacker's objective is determined by its own valuation of the system and target of the attack, which is not necessarily consistent with the defender's utility. If the attacker unexpectedly targets a different utility, then the defense strategy might no longer be optimal. In particular, the defense strategy could be inferior if the attacker's utility is not known to the defender. This study considers a situation where the defender's utility is the system survivability and the attacker's utility is the expected number of destroyed elements in the system. We investigate possible attack strategies under these two different utilities and compare (a) the conservative defense strategy when the attack utility is unknown to the defender with (b) the optimal defense strategy when the attack utility is known to the defender. We show that the conservative protection strategy is still optimal under asymmetric utilities when the contest intensity is smaller than one.