Inspection Games over Time: Classification of Inspection Schemes and Resulting Models

An inspection game is a mathematical model of a situation where a person or an organization, in the following called Inspectorate, verifies that another party, maybe a person, an organization or even a State, and in the following called Operator, adheres to certain agreed or legal rules. The Operator may, however, have an interest in violating these agreed rules. Typically, the Inspectorate's resources are limited so that verification can only be partial. A mathematical analysis helps in designing an optimal inspection scheme, where it must be assumed that an illegal activity is planned strategically. This defines a game theoretical problem between the two players, Operator and Inspectorate.Generally, inspection games over time, i.e. games in which timing aspects are the basis for the objective function, can be characterized along four dimensions: Inspection philosophy (playing for time vs. critical time), timing of interim inspections (discrete time vs. continuous time), planning aspects (non-sequential vs. sequential decision making), and statistical sampling (consideration of statistical errors), leading to about 64 possible models.The aim of this paper is threefold: First, the four dimensions and their consequences on the inspection models are discussed. Second, the situation in which the Operator’s illegal activity needs to be detected within a critical time is analysed, and the sensitivity of the optimal inspection strategies depending on the model assumptions is demonstrated. Third, the transfer in real inspection situations is outlined.