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.