About Inspection Games

Inspection games are an area of application of Game Theory. An inspection game is a mathematical model of a situation where an inspector verifies if one other party, called violator, adheres to certain legal rules. Typically, the inspector's resources are lim­ ited so that verification can only be partial. A game­theoretic model may contribute in designing an optimal inspection scheme. In this scheme, we assume that an illegal action represents a strategic choice of the violator and an inspection represents a strate­ gic choice of the inspector. Thus, one may define a game­theoretic problem, played in stages, with two players, the inspector and the violator. The inspection game was first studied by Melvin Dresher and Michael Mashler in the 1960s. Several variants of inspection games have been studied since then. Be­ sides the fundamental work of M. Dresher (1962) and M. Mashler (1966), we make a short presentation of relevant works of Bernhard von Stengel (2016), Minoru Sak­ aguchi (1977 and 1994) and Thomas Ferguson­Costis Melolidakis (1998). The main object of the present thesis is to study the model introduced by Ferguson and Melolidakis (1998) and an open problem mentioned there. We came up with some interesting results in relation to the behavior of the players and, as a consequence, to the value of the game.