Blameworthiness in Security Games

Security games are an example of a successful real-world application of game theory. The paper defines blameworthiness of the defender and the attacker in security games using the principle of alternative possibilities and provides a sound and complete logical system for reasoning about blameworthiness in such games. Introduction In this paper we study the properties of blameworthiness in security games (von Stackelberg 1934). Security games are used for canine airport patrol (Pita et al. 2008; Jain et al. 2010), airport passenger screening (Brown et al. 2016), protecting endangered animals and fish stocks (Fang, Stone, and Tambe 2015), U.S. Coast Guard port patrol (Sinha et al. 2018; An, Tambe, and Sinha 2016), and randomized deployment of U.S. air marshals (Sinha et al. 2018). Defender \Attacker Terminal 1 Terminal 2 Terminal 1 20 120 Terminal 2 200 16 Figure 1: Expected Human Losses in Security Game G 1. As an example, consider a security game G 1 in which a defender is trying to protect two terminals in an airport from an attacker. Due to limited resources, the defender can patrol only one terminal at a given time. If the defender chooses to patrol Terminal 1 and the attacker chooses to attack Terminal 2, then the human losses at Terminal 2 are estimated at 120, see Figure 1. However, if the defender chooses to patrol Terminal 2 while the attacker still chooses to attack Terminal 2, then the expected number of the human losses at Terminal 2 is only 16, see Figure 1. Generally speaking, the goal of the defender is to minimize human losses, while the goal of the attacker is to maximize them. However, the utility functions in security games usually take into account not only the human losses, but also the cost to protect and to attack the target to the defender and the attacker respectively.