Target-Hardening Decisions Based on Uncertain Multiattribute Terrorist Utility

We present a game-theoretic model to explore how uncertainty about terrorist preferences can affect optimal resource allocations for infrastructure protection. We consider a dynamic game with incomplete information, in which the defender chooses how to allocate her defensive resources, and then an attacker chooses which target to attack according to a multiattribute utility function. Our model constructs a prior distribution representing both defender uncertainty about the attacker weights on the various attributes in the attacker utility function and also defender ignorance about unobserved attributes that may be important to the attacker but have not been identified by the defender. The incorporation of unobserved attributes is a novel feature of our model and allows every target to have a positive prior probability of being attacked when the defender is sufficiently uncertain about the attacker preferences. In a dynamic environment, the defender then has an opportunity to jointly update her knowledge about both the attribute weights and unobserved attributes in a Bayesian manner, based on actual (or attempted) attacks observed in a previous period of the game. In general, defender uncertainty has a greater impact on defensive resource allocations in our model than in much of the previous work.