  This paper studies the optimal mechanisms for the vertically integrated utility to dispatch and incentivize the third-party demand response (DR) providers in its territory. A framework is proposed, with three-layer coupled Stackelberg and simultaneous games, to study the interactions and competitions among the profit-seeking process of the utility, the third-party DR providers, and the individual end users (EUs) in the DR programs. Two coupled single-leader-multiple-followers Stackelberg games with a three-layer structure are proposed to capture the interactions among the utility (modeled in the upper layer), the third-party DR providers (modeled in the middle layer), and the EUs in each DR program (modeled in the lower layer). The competitions among the EUs in each DR program is captured through a non-cooperative simultaneous game. An inconvenience cost function is proposed to model the DR provision willingness and capacity of different EUs. The Stackelberg game between the middle-layer DR provider and the lower-layer EUs is solved by converting the original bi-level programming to a singlelevel programming. This converted single-level programming is embedded in an iterative algorithm toward solving the entire coupled games framework. Case studies are performed on IEEE 34-bus and IEEE 69-bus test systems to illustrate the application of the proposed framework. 
Optimal Utilization of Third-Party Demand Response Resources in   Vertically Integrated Utilities: A Game Theoretic Approach