An Inspection Game with Smuggler’s Decision on the Amount of Contraband

This paper deals with an inspection game of Customs and a smuggler. Customs has two options: patrol or no-patrol. The smuggler makes a decision on the amount of contraband to smuggle. In a given period of days, Customs has a limited number of opportunities to patrol while the smuggler can ship any amount of contraband as long as he has not exhausted this supply. When both players take action, there are some possibilities that Customs captures the smuggler and there are also possibilities that the smuggler is successful. If the smuggler is captured or there remains no day for playing the game, the game ends. In this paper, we formulate the problem as a multi-stage two-person zero-sum stochastic game, derive a closed form of equilibrium in a specific case and investigate the properties of the optimal strategies for the players. Nearly all past research has studied the smuggler’s strategy with the two choices of smuggling or no-smuggling. This paper focuses on the smuggler’s decision as to the amount of contraband.