  This paper considers the remote state estimation in a cyber-physical system
(CPS) using multiple sensors. The measurements of each sensor are transmitted
to a remote estimator over a shared channel, where simultaneous transmissions
from other sensors are regarded as interference signals. In such a competitive
environment, each sensor needs to choose its transmission power for sending
data packets taking into account of other sensors' behavior. To model this
interactive decision-making process among the sensors, we introduce a
multi-player non-cooperative game framework. To overcome the inefficiency
arising from the Nash equilibrium (NE) solution, we propose a correlation
policy, along with the notion of correlation equilibrium (CE). An analytical
comparison of the game value between the NE and the CE is provided,
with/without the power expenditure constraints for each sensor. Also, numerical
simulations demonstrate the comparison results.
