Applying a one-shot and infinite repeated inspection game to materials management

An inspection game models a conflict situation between an inspector and an inspectee. The mathematical analysis aims to determine optimal behaviour of the inspectee. In this paper, the controller’s (inspector) job is to audit a planner’s (inspectee) decision with regard to its optimality and to submit a report to the company’s top managers. Based on Fandel and Trockel (Int J Prod Econ 133:256–261, 2011) this inspection game is discussed here as an infinite two-person game under the aspect of costs minimization. The results show that a higher costs deviation because of a competitive behaviour of the strategic players will decrease their payoffs, so that the optimal cooperative behaviour will finally lead to a better solution for the company with respect to cost minimization as normally expected.