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The Quorum-based Power Saving (QPS) protocols have been proposed to increase the energy efficiency of wireless communication. However, it remains challenging to apply existing QPS protocols to the Mobile Ad Hoc Networks (MANETs) as the timers of nodes are usually asynchronous, the incurred delay are expected to be adaptive, and the network topology is asymmetric. In this paper, we propose an Asynchronous, Adaptive, and Asymmetric (AAA) power management protocol that fulfills the unique requirements of MANETs. We present the asymmetric grid quorum system, a generalization of traditional grid-based quorum systems, to ensure the network connectivity. Theoretical analysis is conducted to demonstrate the benefits of AAA over previous arts.