We consider remote state estimation of cyberphysical systems under signal-to-interference-plus-noise ratio-based denial-of-service attacks. A sensor sends its local estimate to a remote estimator through a wireless network that may suffer interference from an attacker. Both the sensor and the attacker have energy constraints. We first study an associated two-player game when multiple power levels are available. Then, we build a Markov game framework to model the interactive decision-making process based on the current state and information collected from previous time steps. To solve the associated optimality (Bellman) equations, a modified Nash Q-learning algorithm is applied to obtain the optimal solutions. Numerical examples and simulations are provided to demonstrate our results.