This paper considers remote state estimation in cyber-physical systems (CPSs) with multiple sensors, where measurements of each sensor are transmitted to the corresponding remote estimator over a shared communication network with interdependent security. A stochastic non-cooperative game framework with asymmetric information is provided, in which each sensor is in pursuit of minimizing the security investment cost on the first stage associated with the expected error covariance as small as possible at the corresponding remote estimator on the second stage. The asymmetry of information among sensors poses a challenge to characterize or compute the Nash equilibria (NE). To overcome the challenge, based on the common information among sensors, the game with asymmetric information is transformed into another game with symmetric information such that a subclass of NE refer to common information based Markov perfect equilibria of the original game can be achieved by using a backward induction algorithm. Finally, a numerical example is presented to verify the obtained results.

中文翻译：

---

相互依赖且相同的 CPS 的安全投资：信息不对称的随机博弈

本文考虑了具有多个传感器的网络物理系统 (CPS) 中的远程状态估计，其中每个传感器的测量结果通过具有相互依赖安全性的共享通信网络传输到相应的远程估计器。提供了一个具有非对称信息的随机非合作博弈框架，其中每个传感器都在追求最小化第一阶段的安全投资成本，与第二阶段对应的远程估计器的预期误差协方差尽可能小。传感器之间的信息不对称对表征或计算纳什均衡 (NE) 提出了挑战。为了克服挑战，基于传感器之间的共同信息，将信息不对称的博弈转化为另一个信息对称的博弈，使得NE的一个子类参考基于公共信息的原始博弈的马尔可夫完美均衡，通过使用反向归纳算法实现。最后，给出了一个数值例子来验证所得到的结果。