A Booby Trap Game

Strategic Defense Against a Resource Gathering Attacker In many real-world security settings, defenders must monitor a space using limited resources while attackers try to exploit gaps in coverage without being detected. The space may be a shop, museum, or airport, where the defenders use hidden cameras to detect thieves or smugglers, who wish to steal items or conceal contraband. To capture this interaction, Lidbetter and Lin present an attacker-defender game in “A Booby Trap Game.” The defender places several hidden traps within a search space, while the attacker selects a subset of that space to exploit. The attacker’s reward is proportional to the size of the selected subset if the subset does not contain any trap; otherwise, the attacker gets nothing. The article presents optimal (max-min/min-max), or near optimal, randomized strategies for both players for various spaces—including circles, line segments, two-connected networks, trees, and arbitrary Lebesgue measurable, path-connected subsets of Euclidean space.