Game design for price based demand response

In this paper, game design for demand response in smart grid from a control perspective is investigated. A pricing scheme is proposed to ensure the efficiency of the Nash equilibrium. The designed game is proven to be a state-based potential game and the stationary state Nash equilibrium is the social optimal solution. An adaptive penalty based pricing mechanism is proposed and adaptive control laws are designed for both the game states and strategies. The convergence of the stationary state Nash equilibrium is guaranteed under the proposed control laws. We also consider a special case with stubborn players in the game and show that the strategies of the rational players converge to the best response strategies. A numerical example is provided to verify the effectiveness of the proposed methods.