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The free-rider problem arises in the provisioning of public resources, when users of the resource have to contribute towards the cost of production. Selfish users may have a tendency to misrepresent preferences-so as to reduce individual contributions-leading to inefficient levels of production of the resource. Groves and Loeb formulated a classic model capturing this problem, and proposed (what later came to be known as) the VCG mechanism as a solution. However, in the presence of heterogeneous users and communication constraints, or in decentralized settings, implementing this mechanism places an unrealistic communication burden. In this paper, we propose a class of alternative mechanisms for the same problem as considered by Groves and Loeb, but with the added constraint of severely limited communication between users and the provisioning authority. When these mechanisms are used, efficient production is ensured as a Nash equilibrium outcome, for a broad class of users. Furthermore, a natural bid update strategy is shown to globally converge to efficient Nash equilibria. Also, upper bounds are provided for the revenue that can be generated by any individually rational mechanism that ensures efficient production at any Nash equilibrium. It is shown that there exist mechanisms in our class that achieve each of the bounds. An extension to multiple public goods with interrelated valuations is also presented.