  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.
