Efficient distributions of arms-control inspection effort

A rule that constrains decision-makers is enforced by an inspector who is supplied with a fixed level of inspection resources – inspection personnel, equipment, or time. How should the inspector distribute its inspection resources over several independent inspectees? What minimum level of resources is required to deter all violations? Optimal enforcement problems occur in many contexts; the motivating application for this study is the role of the International Atomic Energy Agency in support of the Treaty on the Non-Proliferation of Nuclear Weapons. Using game-theoretic models, the resource level adequate for deterrence is characterized in a two-inspectee problem with inspections that are imperfect in the sense that violations can be missed. Detection functions, or probabilities of detecting a violation, are assumed to be increasing in inspection resources, permitting optimal allocations over inspectees to be described both in general and in special cases. When detection functions are convex, inspection effort should be concentrated on one inspectee chosen at random, but when they are concave it should be spread deterministically over the inspectees. Our analysis provides guidance for the design of arms-control verification operations, and implies that a priori constraints on the distribution of inspection effort can result in significant inefficiencies.