Large-scale demand response (DR) is a useful regulatory method used in high proportion renewable energy sources (RES) integration power systems. Current incentive-based DR schemes are unsuitable for large-scale DR due to their centralized formulation. This paper proposes a distributed scheme to support large-scale implementation of DR. To measure DR performance, this paper proposes the customer directrix load (CDL), which is a desired load profile, to replace the customer baseline load (CBL). The uniqueness of CDL makes it more suitable for distributed schemes, while numerous CBLs have to be calculated in a centralized manner to ensure fairness. To allocate DR tasks and rebates, this paper proposes a distributed approach, where the load serving entity (LSE) only needs to publish a total rebate and corresponding CDL. As for each customer, s/he needs to claim an ideal rebate ratio that ranges from 0 to 1, which indicates the proportion of rebate s/he wants to get from LSE. The rebate value for each customer also determines his or her DR task. Then, the process of customer claims for the ideal rebate ratio is modeled as a non-cooperative game, and the Nash equilibrium is proved to exist. The Gossip algorithm is improved in this paper to be suitable for socially connected networks, and the entire game process is distributed. Finally, a large-scale DR system is formulated. The simulation results show that the proposed DR can promote the consumption of RES. Additionally, this scheme is suitable for large-scale customer systems, and the distributed game process is effective.