## 1 Introduction
While in [26], a Stackelberg game model was formulated between DR aggregator and electricity generators, in which DR aggregator played as the leader to make demand reduction bids, and generators played as followers to compete for maximizing their profits. The above referred papers are all developed on basis of the complete information. However, since much information in reality is unknown to all participants in the market or many participants refuse to share their private information, consequently, each participant in the market does not have information about other opponents in terms of cost functions or payoffs. Therefore, the complete information approach is not suitable for the situation with incomplete information. Based on the background, this paper mainly concentrates on the optimization of bidding strategy for community operators (i.e., DR aggregator) in DR market considering the incomplete information. Here, bidding strategy mainly refers to planning DR resource which will be sold to DR purchaser by DR aggregator in real-time scheduling. By formulating the incomplete information game model, community operators can obtain the optimal profit in the bidding market by speculating opponents' information. In our proposed scenario, community operator is a commercial organization who aggregates DR resource of residential community to participate in the market bidding by signing the contract with users to obtain the control of appliances. Considering DR resource's breach due to the consumption randomness of users, some community operators will equip auxiliary equipment (e.g., energy storage or gas boiler) to compensate the breach amount to enhance DR resource quality. Here, DR resource's breach mainly refers to breach behavior of users who have signed contract with aggregator but refuse to be in DR. Community operators with different auxiliary equipment, which can be divided into different types, will have different quality characteristics of DR resource. In order to protect the privacy of market participants, DR market will not broadcast the information about community operators' types. While in DR market, the payoff of community operator is correlated with the price of DR resource that will be influenced by the grade of DR resource and bidding amount of market participants. Hence, each community operator can know its own payoff but cannot acknowledge other opponents' payoffs completely because their concrete type is not public information. For that, it is necessary for a community operator to model its opponents' expected payoffs according to the probability distribution on opponents' types. That is, Bayesian game approach will be employed to formulate the bidding optimization model in the paper. In brief, the contributions of this paper are as follows. 1. A DR framework is proposed to optimize the bidding strategy of DR resource for community operators considering the risk of DR resource's breach. 2. A Bayesian game based approach is formulated for the proposed scenario with incomplete information to promote the participants' profit, and then an iterative algorithm is designed to obtain the bidding equilibrium among community operators. 3. A case study is carried out to verify the performance and effectiveness of the proposed Bayesian game approach by simulating the bidding strategy optimization of 3 community operators. The proposed DR framework is introduced in Section 2. In Section 3, system model is formulated. Section 4 focuses on the formulation of Bayesian game among community operators. Then, case study is presented in Section 5. Finally, this paper is concluded in Section 6.