Sensors are energy constrained, which leads to possible selfishness as the sensor may decline to forward packets for other nodes. Sensors also face the problem of unfair depletion of their energy if communication protocols were energy-unaware. To address the above concern, we propose the dynamic Bayesian game approach: our algorithm derives mutually acceptable path selection strategies between the sensor and its neighbor, thereby resulting in fairer use of their energy. We validate the feasibility of this technique via analysis and simulations. The results show that it can efficiently handle the sensor's changes in energy and mobility while improving the energy efficiency-network lifetime.