Studying the possibility of a p-type conduction mechanism in the Ag-doped ZnO can clarify persisting ambiguities in the related materials and devices. Here, utilizing the first principles study by hybrid functional calculations, we conclude that the potential acceptor defects Ag_Zn and V_Zn are rare in the low Fermi level conditions required for p-type conduction and, hence, can hardly contribute to the hole generation in ZnO regardless of the assumed O-rich condition. Our results also reveal the exothermicity of the reaction between V_O and Ag_Zn to form the complex defect V_O–2Ag_Zn which is shown to be a less effective donor than V_O. The conversion of the V_O to a less electronically effective complex defect is proposed as the mechanism responsible for the conductivity instabilities in the silver doped zinc oxide.