In this paper, we consider a multi-sensor transmission power control problem in a remote state estimation scenario over a signal-to-noise-and-interference-based communication channel. Multiple sensors send their state measurement data to a remote estimator using a shared wireless communication channel. Since the transmission process of one sensor may be affected by the transmission power used by other sensors, all the sensors need to optimize their transmission strategies to achieve better performance. We formulate Markov decision process and Markov game frameworks to investigate the optimal transmission strategies for the sensors, develop several structural results on the optimal solutions, and then propose two heuristic transmission strategies for easier implementation. Simulation examples are provided to illustrate the main results. (C) 2018 Elsevier Ltd. All rights reserved.