A novel semi-decentralized control strategy is proposed for the integration in the power system of large populations of flexible loads, such as electric vehicles and “smart” appliances. To characterize the interactions between the single agents and their effects on the grid, a game theory framework is adopted. The price responsive appliances are modelled as competing players, characterizing a stable and efficient solution as a Nash equilibrium (no device has unilateral interest in changing its scheduled power consumption when the final electricity price is considered). We extend previous results on distributed control of flexible demand, proposing a partial centralization of the power scheduling at critical time instants. In this way, it is possible to ensure convergence to a Nash equilibrium for a wider range of scenarios, considering higher penetration levels of flexible demand and a wider range of parameters for the devices. The effectiveness of the proposed scheme is theoretically proved and its performance is evaluated in simulations, considering a future UK grid with high penetration of flexible demand.