Access to alternative energy sources provides consumers with a way to not only be energy efficient but also restrict the amount of information potentially shared with electricity providers via smart meters. On the other hand, electricity providers require certain amount of energy to be consumed directly from the grid in order to perform load forecasting and maintain stable and reliable operation. Therefore, the electricity provider may need to offer incentives to encourage consumers to consume a desired level of energy directly from the grid. Each consumer faces a trade-off between masking consumption from the electric power grid for privacy reasons and revealing consumption patterns to the electricity provider for energy cost reduction. In this paper, we present a game theoretic approach to design price-based incentives for consumers that balance their privacy concerns against the electricity provider's needs. Under certain conditions, we show the existence and uniqueness of the nondegenerate mixed strategy Nash equilibrium and study the relationship between incentive prices from the electricity provider and responses from privacy-sensitive consumers. Simulation results indicate that the proposed mechanism can benefit both electricity providers and consumers.