A commonly employed abstraction for studying the object placement problem for the purpose of Internet content distribution is that of a distributed replication group. In this work the initial model of distributed replication group of Leff, Wolf, and Yu (IEEE TPDS '93) is extended to the case that individual nodes act selfishly, i.e., cater to the optimization of their individual local utilities. Our main contribution is the derivation of equilibrium object placement strategies that: (a) can guarantee improved local utilities for all nodes concurrently as compared to the corresponding local utilities under greedy local object placement; (b) do not suffer from potential mistreatment problems, inherent to centralized strategies that aim at optimizing the social utility; (c) do not require the existence of complete information at all nodes. We develop a baseline computationally efficient algorithm for obtaining the aforementioned equilibrium strategies and then extend it to improve its performance with respect to fairness. Both algorithms are realizable in practice through a distributed protocol that requires only limited exchange of information.