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Frequency hopping-based antijamming techniques are not always applicable in vehicular ad hoc networks (VANETs) due to the high mobility of onboard units (OBUs) and the large-scale network topology. In this paper, we use unmanned aerial vehicles (UAVs) to relay the message of an OBU and improve the communication performance of VANETs against smart jammers that observe the ongoing OBU and UAV communication status and even induce the UAV to use a specific relay strategy and then attack it accordingly. More specifically, the UAV relays the OBU message to another roadside unit (RSU) with a better radio transmission condition if the serving RSU is heavily jammed or interfered. The interactions between a UAV and a smart jammer are formulated as an antijamming UAV relay game, in which the UAV decides whether or not to relay the OBU message to another RSU, and the jammer observes the UAV and the VANET strategy and chooses the jamming power accordingly. The Nash equilibria of the UAV relay game are derived to reveal how the optimal UAV relay strategy depends on the transmit cost and the UAV channel model. A hotbooting policy hill climbing-based UAV relay strategy is proposed to help the VANET resist jamming in the dynamic game without being aware of the VANET model and the jamming model. Simulation results show that the proposed relay strategy can efficiently reduce the bit error rate of the OBU message and thus increase the utility of the VANET compared with a Q-learning-based scheme.