As competition is introduced across the electric power industry around the world, market design for the industry is urgently needed to shape its future structure and performance. When generator companies compete with one another in a deregulated market, they may not be willing to share the information needed to perform an economic dispatch of the generation. Using game theory, this paper designs a new mechanism that achieves efficiency (economic dispatch) in spite of this information problem. In this mechanism, when each company acts in the best of its own interests, the outcome is efficient. The paper demonstrates the merits of the mechanism by simulations including the IEEE 14-bus case.