Confronting an enemy with unknown preferences: Deterrer or provocateur?

Nation 1 is seeking to join the nuclear club. Nation 2, its enemy, would like to prevent this, and has the potential to destroy 1's bomb-making facilities. It is uncertain whether 1 has a bomb. So are its intentions. 1 could be seeking to deter an attack. Alternatively, if no bomb is present, 1 might wish to provoke one as a means to secure support at home and abroad. Lacking a bomb, 1 can avoid an attack by allowing inspections. If it refuses inspections, 2 must rely on its imperfect intelligence system to determine whether to attack. This game has a unique sequential equilibrium, possibly separating, possibly pooling. At that equilibrium there is a positive probability that: No bomb is built; 2's intelligence system accurately detects no bomb; 1 refuses inspections; nevertheless 2 attacks. Present and past experiences form Iraq, Iran, Syria, and North Korea illustrate the analysis.