Attacking the unknown weapons of a potential bomb builder: The impact of intelligence on the strategic interaction

Nation 1 wants to develop a nuclear bomb (or other weapons of mass destruction). Nation 2, its enemy, wants to prevent this, either by requiring that 1 open his facilities, or through a pinpoint strike if her imperfect intelligence system (IS) indicates a bomb is present or imminent. If 1 refuses full inspection, 2 can attack 1 or not. 1's cost for allowing inspection, private information, can be either high, H, or low, L. The game's unique sequential equilibrium will be separating or pooling, depending on the precision of IS. The equilibrium is fully characterized. Surprisingly for less accurate IS, 2 behaves aggressively - her appetite to attack is strong. Highly accurate IS dampens that appetite. The following tragic outcome arises in equilibrium with positive probability: 1 does not develop the bomb; 2's IS correctly signals 1's decision; 1, regardless of type, refuses to open its facilities; 2 attacks 1.