Lexicographic programming for solving security game with fuzzy payoffs and computing optimal deception strategy

Abstract

Today, security and peace in different parts of society is one of the most important issues of mankind. Especially, due to the expansion of communications, the increase in international flights, and the development of transportation, the need to security is felt more than before. Achieving this requires predicting and preventing riots or attacks on various centers using scientific techniques. On the other hand, the limitations of security resources, including manpower and military facilities, have to be considered. Another challenge of security forces is that attackers observe the pattern of security forces before planning any attack. Therefore, defensive forces have to take into account the attacker's priorities in their decision making. Game theory provides a mathematical approach to utilize some limited security resources to maximize their efficiency. In this paper, a mathematical model is proposed to optimize the­­­ allocation of the forces, using a game theory analysis. Naturally, each player is unaware of the importance of targets for the other, exactly. In this model, in order to handle the players' uncertainty about the importance of targets, their payoffs are considered as triangular fuzzy numbers. Then, Lexicographic optimization is applied to solve the problem using an ordering relation on triangular fuzzy numbers. The final part of the paper deals with solving the security game problem with deceptive resources in the fuzzy environment in which, the defender can also use unrealistic resources to reduce the attacker's productivity, given the available budget.

Keywords

• stackelberg game
• security game
• optimal allocation of force
• deceptive resources
• fuzzy theory