A smuggling game with asymmetrical information of players

Abstract

This paper deals with a smuggling game with multiple stages. Customs is allowed to patrol within the limited number of chances and obtain reward by the capture of a smuggler. The smuggler gets a reward depending on the amount of contraband he succeeds to ship in smuggling at each stage. The pay-off of the game is zero-sum. In almost all past studies, they adopt the alternative of smuggling or non-smuggling as the smuggler's strategy. From the point of view of information, some researchers assumed that both players could observe their opponent's behaviour at the past stage or a few assumed that both players had no information about their opponent. Other than these types of smuggling games with the symmetric information, we introduce the asymmetrical acquisition of information or the concept of perfect Bayesian equilibrium in the smuggling game for the first time.

Keywords:

• game theory
• linear programming
• military
• decision analysis