A Study on a Sequential One-Defender-N-Attacker Game

Government usually faces threat from multiple attackers. However, in the literature, researchers often model attackers as one monolithic player who chooses whether to attack, how much investment to spend, and on which target, instead of treating multiple attackers as independent agents. This modeling strategy may potentially cause suboptimal defense investment if the attackers have vastly different interests and preferences and may not be combined as one in theory. In this article, we develop a sequential game with complete information. This model considers one defender explicitly dealing with multiple unmergeable attackers. Thorough numerical experiments are conducted using ratio and exponential contest success functions under different scenarios. The result is also contrasted with the corresponding single attacker model to study the effect of mishandling multiple attackers. The propositions and observations drawn from the numerical experiments provide insights for government decision making with a better understanding of the attackers' behavior.