The reputation-based trust mechanism is a way to assess the trustworthiness of offered services, based on the feedback obtained from their users. In the absence of appropriate safeguards, service users can still manipulate this feedback. Auction mechanisms have already addressed the problem of manipulation by market-trading participants. When auction mechanisms are applied to trust systems, their interaction with the trust systems and associated overhead need to be quantitatively evaluated. This paper proposes two distributed architectures based on centralized and hybrid computing for integrating an auction mechanism with the trust systems. The empirical evaluation demonstrates how the architectures help to discourage users from giving untruthful feedback and reduce the overhead costs of the auction mechanisms.