Peer to peer (P2P) networks are built to operate without any central or trusted authority. Those networks are used in many systems and applications (e.g. Bitcoin, BitTorrent, DHTs). One major limitation of open P2P networks is the lack of strong identities, that allows any potential attacker to create many identities in the system. Such attacks can be used to disrupt the P2P overlay’s connectivity, and to sabotage its operation. In this paper, we search for new ways to construct network topologies that will be resilient to such attacks. We investigate a game theoretic approach to the overlay construction problem when attackers try to disconnect certain defender nodes. We utilize several cost models for the attack that rely on network topology or other underlying network properties that the attacker cannot easily fake, such as its IP address, or ping RTT.