In this paper an efficient energy curtailment scheme is studied, which enables the power users of a smart grid network to decide on the reduction in energy supplied to them in the event of a power outage in the system. Considering the advantages of a two-way communications infrastructure for any future smart grid, a non-cooperative generalized Nash game is proposed where the players are users of power in the network. They adopt a strategy to choose the amount of reduction in energy supplied to them based on their energy requirements so as to minimize the total cost incurred to the system due to the power outage (i.e., social optimality). The game is modeled as a variational inequality problem, and it is shown that the socially optimum solution is obtained at the variational equilibrium of the energy curtailment game. An algorithm that enables the users to efficiently reach this equilibrium is proposed. Simulation results show that the proposed game yields an improvement of about 15% on average, in terms of average total cost reduction, compared to a standard equal power curtailment scheme.