In a fully distributed peer-to-peer (P2P) overlay network, peer processes (peers) cannot perceive where every object exists due to the scalability and openness. A peer has to obtain service through communicating with acquaintance peers. Here, acquaintance peers may hold obsolete information and may be even malicious. Hence, it is critical for a peer to identify which acquaintance is more trustworthy. In this paper, the trustworthiness of an acquaintance is defined in terms of the satisfiability and ranking factor. We define how satisfiable a requesting peer is for each type of access requests by newly taking into account the authorization. The ranking factor of an acquaintance shows how much the acquaintance is trusted by trustworthy acquaintances. The trustworthiness of each acquaintance is propagated in a peer-by-peer way. We evaluate how the ranking factors of acquaintances are changing in presence of faulty peers.