In many communications settings, such as wired and wireless local-area networks, when multiple users attempt to access a communication channel at the same time, a conflict results and none of the communications are successful. Contention resolution is the study of distributed transmission and retransmission protocols designed to maximize notions of utility such as channel utilization in the face of blocking communications. An additional issue to be considered in the design of such protocols is that selfish users may have incentive to deviate from the prescribed behavior, if another transmission strategy increases their utility. The work of Fiat et al.  addresses this issue by constructing an asymptotically optimal incentive-compatible protocol. However, their protocol assumes the cost of any single transmission is zero, and the protocol completely collapses under non-zero transmission costs. In this paper, we treat the case of non-zero transmission cost c. We present asymptotically optimal contention resolution protocols that are robust to selfish users, in two different channel feedback models. Our main result is in the Collision Multiplicity Feedback model, where after each time slot, the number of attempted transmissions is returned as feedback to the users. In this setting, we give a protocol that has expected cost 2n+clogn and is in o(1)-equilibrium, where n is the number of users.