A compulsory smuggling model of inspection game taking account of fulfillment probabilities of players' aims

This paper deals with an inspection game of the customs and a smuggler. The customs can take two options of assigning a patrol or not. The smuggler has two strategies of shipping its cargo of contraband or not. Two players have several opportunities to take an action during a limited number of days but only the smuggler cannot discard any opportunity intentionally. When the smuggling coincides with the patrol, there are three possibilities: that the customs captures the smuggler, the smuggler makes a success of the smuggling or that neither of them happens. If the smuggler is captured or there remain no day for playing the game, the game ends. There have been some studies so far on the inspection game. Some consider the cases that the smuggler has only one smuggling or the perfect-capture case that the customs can certainly arrest the smuggler on patrol, and others think of a recursive game without the probabilities of fulfilling players' purposes. However there has been little study in which they discussed the stochastic inspection. In this paper we formulate the problem into multi-stage two-person zero-sum stochastic game and investigate some characteristics of its equilibrium solution, some of which are given in closed forms in special cases.