Unstructured networks (like ad-hoc or peer-to-peer networks) are networks without centralized control of their operation. Users make local decisions regarding whether to follow the network protocol or not. While providing scalability benefits, this degrades the performance, which is compounded by the potential presence of Malicious Users. In general, these users are trying to disrupt the operation of the network, and prevent the legitimate users from achieving their objectives. More specifically, they could try to break the connectivity of the network, or waste the resources of the legitimate users. In this work we use game theory to examine the effect of Malicious Users. All users are modeled as payoff-maximizing strategic agents. A simple model, fictitious play, is used for the legitimate user behavior, but no limits are imposed on the Malicious Users strategies. We look for the worst case equilibrium: the one that gives Malicious Users the highest payoff. We identify the importance of the network topology.