Research on security in Peer-to-Peer (P2P) systems is dominated by reputation-based solutions. These solutions propagate opinions about other peers in order to help identify the best set of peers to utilize. In this paper, we model peers with utility functions and use those functions to examine the case in which an individual peer participates in an unfamiliar and untrusted system, similar to one in which a mobile peer can enter when moving into a new location. We additionally introduce a novel security mechanism for P2P systems called resource exploration in order to mitigate the problems inherent in reputation-based systems and analyze its effect on a 2-player game (between an attacker and the benign peer).