A major limitation of open P2P networks is the lack of strong identities. This allows any agent to attack the system by creating multiple false personas, thereby disrupting the overlay network's connectivity and sabotaging its operation. In this paper, we explore practical ways to defend P2P networks from such attacks. To do so, we employ a game theoretic approach to the management of each peer's list of known nodes and to the overlay construction mechanisms that utilize this list. We consider the interaction between defender and attacker agents as a zero-sum game. We show that the cost of attacks can be driven up substantially if the defender utilizes available information about peers it chooses to connect to, such as their IP address. In addition to theoretical analysis of the underlying game, we apply our approach to the Bitcoin P2P network and derive effective strategies that guarantee a high safety level against attacks.