Optimal Enforcement and Adequate Penalties

When inspection is used to enforce a rule in a context such as arms control, auditing, or food and drug inspection, there is a conflict between inspector and inspectee that can be modeled as a non-zerosum strategic-form game. Suppose that the inspectee may violate at any subset of n non-identical “sites”, complying at the rest. The inspector chooses k < n sites at which to assess the inspectee’s behavior. We assume that inspections are perfect in that a violation at an inspected site is always detected, and false alarms never occur, and say that the violation penalty is adequate if the inspector can select an inspection strategy that rationally induces the inspectee to comply at all sites. We determine these optimal inspection strategies in important classes of inspection games, thereby identifying the minimum adequate penalty, or threshold. We then study how the threshold is related to other parameters, principally the amount of inspection (represented by k), which is an important issue for treaty designers and policy-makers.