Allocating Defensive Resources with Private Information about Vulnerability

In many resources-allocation problems, strategic adversaries move sequentially and are likely to have private information about the effectiveness of their spending. A defender, for example, often has to allocate its defensive resources before an attacker (e.g., a terrorist group) decides where to strike. Defenders are also likely to have private information about the vulnerability of the things they are trying to protect. Sequential decisions and private information about effectiveness creates a dilemma for a defender. Allocating more to a highly vulnerable site reduces the expected losses should that site be attacked but may also signal that that site is more vulnerable and thereby increase the probability of an attack. Modeling this tradeoff as a signaling game, the analysis shows that secrecy concerns generally swamp vulnerability concerns when more vulnerable sites are weakly harder to protect on the margin. The defender pools in equilibrium, that is, allocates its resources in the same way, regardless of the level of vulnerability. If more vulnerable sites are easier to protect on the margin, vulnerability concerns may swamp secrecy concerns.