Chapter 51 Inspection games Starting with the analysis of arms control and disarmament problems in the sixties inspection games have evolved into a special area of game theory with specific theoretical aspects and equally important practical applications in various fields of human activity where inspection is mandatory. In this contribution a survey of applications is given first. These include arms control and disarmament theoretical approaches to auditing and accounting for example in insurance and problems of environmental surveillance. Then the general problem of inspection is presented in a game theoretic framework that extends a statistical hypothesis testing problem. This defines a game since the data can be strategically manipulated by an inspectee who wants to conceal illegal actions. Using this framework two models are solved which are practically significant and technically interesting: material accountancy and data verification. A second important aspect of inspection games is the fact that inspection resources are limited and have to be used strategically. This is demonstrated in the context of sequential inspection games where many mathematically challenging models have been studied. Finally the important concept of leadership where the inspector becomes a leader by announcing and committing himself to his strategy is shown to apply naturally to inspection games.