Today's electric power grid aims to provide reliable power service that meets (even the most rarely occurring) demand peaks. Consequently, this necessitates the grid be equipped with ample generation sources that can be costly and unsustainable. Demand response (DR) is one popular approach to reduce peak demand that requires communications and coordination amongst DR participants. In this paper, we propose a novel distributed DR strategy that employs simplistic cost signals broadcasted by the electric power utility for coordination and convergence to a desired aggregate peak demand reduction. We make use of evolutionary game theoretic concepts to analytically and empirically establish important convergence properties. Our results indicate that our strategy is real-time and highly scalable demonstrating promise for practical deployment.