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We use a Bayesian game-theoretic approach to model transmission control in energy-harvesting wireless sensor networks. In general, the energy state of an energy-harvesting sensor varies more dramatically with time as compared to traditional battery-powered sensors. Therefore, each energy-harvesting sensor is aware of its instantaneous energy state, which is modeled as its private information. Each sensor decides its transmission strategy according to its belief of its opponents' energy states. There exists a Bayesian Nash equilibrium (BNE) where a sensor with energy higher than its energy threshold will decide to transmit at fixed power, and wait otherwise. We show how each sensor determines its threshold to maximize its utility function. Moreover, we show via simulations that the performance of the Bayesian game model is close to that of a perfect-information game where energy states are common information to all sensors. In addition, since the proposed Bayesian game has the advantage of requiring less information exchange overhead, it seems to be more feasible to implement than the perfect-information game.