## 5 Networked ATM-CPS Game Model
### A Game Modeling Method of Networked ATM-CPS Based on Bayesian Nash Equilibrium Strategy
Using temporal logic and model checking methods, the security threats of networked ATM system are studied at a higher level of abstraction. Further, the security requirements of ATM can be explored and the security requirements modeling method based on CPS features can be studied. Use the CPS system model and security requirements of the previously constructed networked ATM system to match all potential attack modes and establish a dynamic Bayesian ATM-CPS game model on the basis of the ATM-CPS security threat model, as shown in Figure 8.  
Figure 8: The ATM-CPS game model. From the perspective of security threats, attacks on the ATM-CPS may have different consequences. For example, the equipment of ATM system is damaged (including overloading of equipment and violation of safety restrictions) or operation loss is caused (i.e., service quality and operation efficiency are reduced). Attackers use the security risks and system vulnerabilities of the ATM-CPS to carry out network hijacking and even some network crimes. Therefore, the security of the ATM-CPS must be evaluated, including the following points. * Simulate the dynamic behavior of the ATM-CPS under normal conditions and the behavior under network attacks. * Study the difference parameters based on ATM and attacker. For example, detection frequency, attacker's understanding of the system, physical damage parameters, and attacker's punishment attack detection results may affect the security of CPS. * Use game theory to study the Bayesian Nash equilibrium strategy of attackers and ATM systems under different interdependence conditions and estimate the attack and detection probability according to special defensive and antagonistic parameters (known and unknown attacks can be detected and identified using intelligent algorithms). * Evaluate the security indicators of the ATM-CPS on the basis of the threat model (e.g., availability, failure time). ATM-CPS game model:  
\[CPS-G_{ATM}=\left\langle S,\sum T,X,G,F,P,A,R\right\rangle \tag{2}\]  
where \(S=\{N,P,W,E,NE,S,R,F\}\) is a set of system states. Among them, \(\mathbf{N}\) is the initial normal state; \(\mathbf{P}\) is the penetration state; \(\mathbf{W}\) is the warning state; \(\mathbf{E}\) is an emergency; \(\mathbf{NE}\) is a non-emergency state; \(\mathbf{S}\) is the stop state; \(\mathbf{R}\) is the recovery state; \(\mathbf{F}\) is the failure status. \(F=\{F_{ATM},F_{attack}\}\) is a set of players, \(F_{ATM}\) is the ATM-CPS, and \(F_{Attack}\) is the attacker. \(P=\{P_{Attack},P_{ATM}\}\) is the action set, \(P_{Attack}\) represents the attacker, and \(P_{ATM}\) represents the ATM-CPS. \(R=\{R_{Attack},R_{ATM}\}\) is a practical program function. \(R_{Attack}\) is used for attackers and \(R_{ATM}\) is used for ATM-CPS. \(T\subseteq S\times\sum\times G\times A\times S\) is a finite set of transitions among states, adding actions of both players to the transition function. According to the current state of the players and the model, the model can be transferred to a new state. Therefore, the ATM-CPS game model is a random mixed model.