Data grids and its cost effective nature has taken on a new level of interest in recent years; amalgamation of different providers results in increased capacity as well as lower energy costs. As a result, there are efforts worldwide to design more efficient data replication algorithms. Such replication algorithm for grids is further complicated by the fact that the different sites in a grid system are likely to have different ownerships with their own self interest and priorities. As such, any replication algorithm that simply aims to minimize total job delays are likely to fail in grids. Further, a grid differs from traditional high performance computing systems in the heterogeneity of the communication links that connect the different nodes together. In this paper, we propose a distributed, non-cooperative game theoretic approach to the data replication problem in grids. Our proposed replication scheme directly takes into account the self interest and priorities of the different providers in a grid, and maximizes the utility of each provider individually. Experiments were conducted to show the applicability of the proposed approaches. One advantage of our scheme is the relatively low overhead and robust performance against inaccuracies in performance prediction information.