  In this work, we use a Stackelberg infinite discrete-time dynamic game model
to study the optimal supply schedule and the optimal demand response under a
market-driven dynamic price. A two-layer optimization framework is established.
At the lower layer, for each user, different appliances are scheduled for
energy consumption. For enegy provider, different generators are utilized for
energy generation. At the upper level, with the supplier acting as a leader and
the users acting as followers, a Stackelberg dynamic game is used to capture
the interaction among the energy provider and the users where the energy
provider and the users care only about their own cost. We analyze the
one-leader-N-followers Stackelberg dynamic game and characterize the
Stackelberg equilibrium. We provide a closed-form Nash solution of the optimal
dynamic demand response problem when the supply is announced. A set of linear
constraints is developed to characterize the Stackeberg equilibrium. Simulation
results show that the price is driven to a reasonable value. Also, the total
demand and the supply is balanced.
