A sequential partial information bomber-defender shooting problem

A bomber carrying homogenous weapons sequentially engages ground targets capable of retaliation. Upon reaching a target, the bomber may fire a weapon at it. If the target survives the direct fire, it can either return fire or choose to hold fire (play dead). If the former occurs, the bomber is immediately made aware that the target is alive. If no return fire is seen, the true status of the target is unknown to the bomber. After the current engagement, the bomber, if still alive, can either re-engage the same target or move on to the next target in the sequence. The bomber seeks to maximize the expected cumulative damage it can inflict on the targets. We solve the perfect and partial information problems, where a target always fires back and sometimes fires back respectively using stochastic dynamic programming. The perfect information scenario yields an appealing threshold based bombing policy. Indeed, the marginal future reward is the threshold at which the control policy switches and furthermore, the threshold is monotonic decreasing with the number of weapons left with the bomber and monotonic nondecreasing with the number of targets left in the mission. For the partial information scenario, we show via a counterexample that the marginal future reward is not the threshold at which the control switches. In light of the negative result, we provide an appealing threshold based heuristic instead. Finally, we address the partial information game, where the target can choose to fire back and establish the Nash equilibrium strategies for a representative two target scenario.     

How do wars end? A multidisciplinary enquiry

ABSTRACT

The cessation of military confrontations rarely coincides with the end of war. Legal and political matters continue after the last shot has been fired, civilians driven from their homes try to rebuild their houses and their lives, veterans need to adapt to their new role in civil society, and the struggle to define the history and the significance of past events only begins. In recent years, in particular, the changes in the character of contemporary warfare have created uncertainties across different disciplines about how to identify and conceptualise the end of war. It is therefore an opportune moment to examine how wars end from a multidisciplinary perspective that combines enquiries into the politics of war, the laws of war and the military and intellectual history of war. This approach enables both an understanding of how ‘the end’ as a concept informs the understanding of war in international relations, in international law and in history and a reconsideration of the nature of scientific method in the field of war studies as such.