Peer-to-Peer networks exist with the volunteering cooperation of various entities on the Internet. Their self-structure nature has the important characteristic that they make no use of central entities to run as coordinators and the benefits of this cooperation can be enjoyed equally by all the members of the community with the assumption that they all make right use of the protocol. In this study we examine what the consequences on the community are in the case of existence of misbehaving nodes which can abuse the network resources for their personal benefit and we also analyze the cost and the benefit of some proposed solution that could be used in order to bring into account the above problem.