The dependence of inspection-system performance on levels of penalties and inspection resources

This paper presents three s imple mathematical models, all of gametheoretic type, dealing with an inspector-inspectee relationship. The inspectee alw ays tries to max imize hi s ne t gain, whic h is the amount he obtain s by "cheatin g" less the amount he is penalized whe n ca ught. The first model assumes a zero-sum payoff and so the in spector tries to minimize the in spectee's ne t ga in . [n the second model, the ins pec tor tries to deter cheat ing wit hout concern fo r the ex tract ion of pe nalties. [n the third mode l we assume that the probabilistic patte rn of the ins pecto r' s stra tegy is know n to the in s pectee and that the inspector constructs hi s strategy with thi s in mind. Each of these mode ls is analyzed and op timal so lutions are obtained . Seve ral s imple exa mples are prese nt ed to show the re lat ion between the level of chea ting and the levels of in s pec tion reso urces and penalty.