Attacking the Unknown Weapons of a Possible Provocateur: How Intelligence Affects the Strategic Interaction

We consider the interaction of two enemy nations. Nation 1 wants to develop a nuclear bomb (or other weapons of mass destruction). Nation 2 wants to prevent such a development through the deterrence of a threatened attack, or an actual attack if it thought the bomb was produced. 2 has an intelligence system that imperfectly indicates the presence of a bomb. 1, if lacking the bomb, can open its facilities to prevent an attack. A further uncertainty is that nation 2 does not know nation 1’s type. He could be a Deterrer, whose prime goal is to avoid an attack, or he could a Provocateur who prefers an unjustified attack if he does not possess the bomb, so as to build support from inside his nation and the outside world. The game has a unique sequential equilibrium. The qualitative nature of that equilibrium depends on parameters, on preferences and information conditions. A number of initially counterintuitive results emerge. For example, it may sometimes be rational (an equilibrium strategy) for 2 to attack even though 1 does ∗Hebrew University of Jerusalem, Israel and Ariel University, Israel, [email protected] †The Interdisciplinary Center, Herzliya, Israel and Stony Brook University, NY, USA,[email protected] ‡Harvard University, USA,Richard [email protected]