Game Theoretical Perspectives for Diversion Path Analysis

Diversion path analysis in the context of nuclear material safeguardsis the identification and evaluation of all paths alongwhich nuclear material can be diverted from the peaceful nuclearfuel cycle for military purposes or purposes unknown. Obviouslysuch an analysis must be strategic in nature, giving particular attentionto those diversion paths that are most promising fromthe diverter’s point of view. This implies, in turn, the use of gametheoretical concepts, a fact that has been long recognized butthat has enjoyed renewed interest in recent years by more andmore analysts. This paper presents a general framework for gametheoretical approaches to diversion path analysis. Starting withthe elementary case of only two paths and very simple payoffsto the inspectorate and the state, it is shown how the problemcan be formulated and solved in terms of game theory. Then thetechnically more difficult generalization to an arbitrary numberof diversion paths is described. The inclusion of additional complicatingaspects in the analysis, such as false alarm and detectionprobabilities, conversion times and inspection effort is examinedand partial solutions are presented, in particular the conditionsunder which the State is deterred from illegal behavior. A discussionof the usefulness of this kind of analysis concludes the paper.IntroductionDiversion path analysis in the context of nuclear material safeguardsis the identification and evaluation of all paths alongwhich nuclear material can be diverted from the peaceful nuclearfuel cycle for military purposes or for purposes unknown. It is immediatelyapparent that such an analysis must be strategic in nature,giving particular attention to those diversion paths that aremost promising from the diverter’s point of view. This implies,in turn, the use of game theoretical concepts, a fact that has beenlong recognized by a few, but that has enjoyed increased interestin recent years by more and more analysts.Diversion path analysis has in fact been performed in variousways for over a decade, see, e.g., References 1, 2, 3 and 4 but theunderlying mathematical structure has been studied for a muchlonger time as a strategic sampling problem. See, e.g., Reference5 where inspection regimes were analyzed in terms of the varyingattractivity of posited illegal activities at different locations, onlya subset of which could be inspected in a given reference time.This analysis was referred to as “global sampling” and from amathematical point of view, diversion path analysis and globalsampling schemes are essentially the same.Quite a number of global sampling models have beendeveloped under different safeguards contexts. It turns out,however, that most of them can be reduced to two basic modelsif one includes the problem of inspection resource distributionover several states.5 Since multiple state problems do notproperly fall into the category of a diversion path model, wedo not consider them here explicitly, but mention them in ourconcluding remarks. It is the purpose of this contribution todevelop the basic model for diversion path analysis and to showhow some of its generalizations can be obtained by simply reinterpretingthe parameters involved. It will also be shown howother generalizations, which also can be deduced from the basicmodel, require some additional modification.By generalization, we mean in the present context beginningfrom a simple model that covers only a few features of an inspectionproblem and then proceeding to add more features, like errorsof the first and second kind, timeliness, etc. This contrasts witha mathematician’s conventional idea of generalization: a simplemodel, which implicitly contains all relevant features in theappropriately defined model parameters, is the most general one.The global sampling approach to nuclear safeguardsproblems.